Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application","authors":"Qingdong Guo ,&nbsp;Ji Li ,&nbsp;Brett D. Wick","doi":"10.1016/j.na.2025.113916","DOIUrl":"10.1016/j.na.2025.113916","url":null,"abstract":"<div><div>In this paper, we establish the Fefferman–Stein type decomposition of the <span><math><mi>CMO</mi></math></span> space in the Dunkl setting. That is <span><math><mrow><mi>f</mi><mo>∈</mo><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> if and only if <span><span><span><math><mrow><mi>f</mi><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><munderover><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></munderover><msub><mrow><mover><mrow><mi>R</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><msub><mrow><mover><mrow><mi>R</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>j</mi></mrow></msub></math></span>, <span><math><mrow><mi>j</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>d</mi></mrow></math></span>, represent the Dunkl–Riesz transforms. Our main tool is to characterize <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> via two approximations, which are new even for the classical space <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. As a direct application of our characterization of <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span>, we prove the duality of <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113916"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local invariants and geometry of the sub-Laplacian on H-type foliations","authors":"Wolfram Bauer ,&nbsp;Irina Markina ,&nbsp;Abdellah Laaroussi ,&nbsp;Sylvie Vega-Molino","doi":"10.1016/j.na.2025.113934","DOIUrl":"10.1016/j.na.2025.113934","url":null,"abstract":"<div><div><span><math><mi>H</mi></math></span>-type foliations <span><math><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>H</mi><mo>,</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>H</mi></mrow></msub><mo>)</mo></mrow></math></span> are studied in the framework of sub-Riemannian geometry with bracket generating distribution defined as the bundle transversal to the fibers. Equipping <span><math><mi>M</mi></math></span> with the Bott connection we consider the scalar horizontal curvature <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> as well as a new local invariant <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span> induced from the vertical distribution. We extend recent results on the small-time asymptotics of the sub-Riemannian heat kernel on quaternion-contact (qc-)manifolds due to A. Laaroussi and we express the second heat invariant in sub-Riemannian geometry as a linear combination of <span><math><msub><mrow><mi>κ</mi></mrow><mrow><mi>H</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>V</mi></mrow></msub></math></span>. The use of an analog to normal coordinates in Riemannian geometry that are well-adapted to the geometric structure of <span><math><mi>H</mi></math></span>-type foliations allows us to consider the pull-back of Korányi balls to <span><math><mi>M</mi></math></span>. We explicitly obtain the first three terms in the asymptotic expansion of their Popp volume for small radii. Finally, we address the question of when <span><math><mi>M</mi></math></span> is locally isometric as a sub-Riemannian manifold to its <span><math><mi>H</mi></math></span>-type tangent group.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113934"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144920377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimizers of mass-constrained functionals involving a nonattractive point interaction","authors":"Gustavo de Paula Ramos","doi":"10.1016/j.na.2025.113905","DOIUrl":"10.1016/j.na.2025.113905","url":null,"abstract":"<div><div>We establish conditions to ensure the existence of minimizer for a class of mass-constrained functionals involving a nonattractive point interaction in three dimensions. The existence of minimizers follows from the compactness of minimizing sequences which holds when we can simultaneously rule out the possibilities of vanishing and dichotomy. The proposed method is derived from the strategy used to avoid vanishing in Adami et al. (2022) and the strategy used to avoid dichotomy in Bellazzini and Siciliano (2011). As applications, we prove the existence of ground states with sufficiently small mass for the following nonlinear problems with a point interaction: a Kirchhoff-type equation and the Schrödinger–Poisson system.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113905"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Singular velocity of the Stokes and Navier–Stokes equations near boundary in the half-space","authors":"Tongkeun Chang,&nbsp;Kyungkeun Kang","doi":"10.1016/j.na.2025.113939","DOIUrl":"10.1016/j.na.2025.113939","url":null,"abstract":"<div><div>Local behavior near the boundary is analyzed for solutions of the Stokes and Navier–Stokes equations in the half space with localized non-smooth boundary data. We construct solutions to the Stokes equations whose velocity fields are unbounded near the boundary away from the support of boundary data, although the velocity and its gradient of solutions are locally square integrable. This is an improvement compared to known results in the sense that the velocity field itself is unbounded, since previously constructed solutions were bounded near the boundary, although their normal derivatives are singular. We also establish singular solutions and their derivatives that do not belong to <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mi>q</mi></mrow></msubsup></math></span> near the boundary for <span><math><mrow><mi>q</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. For such examples, the corresponding pressures turn out not to be locally integrable. A similar construction, via a perturbation argument, is available to the Navier–Stokes equations near the boundary as well.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113939"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The superposition principle for local 1-dimensional currents","authors":"L. Ambrosio,&nbsp;F. Renzi,&nbsp;F. Vitillaro","doi":"10.1016/j.na.2025.113913","DOIUrl":"10.1016/j.na.2025.113913","url":null,"abstract":"<div><div>We prove that every one-dimensional locally normal metric current, intended in the sense of U. Lang and S. Wenger, admits a nice integral representation through currents associated to (possibly unbounded) curves with locally finite length, generalizing the result shown by E. Paolini and E. Stepanov in the special case of Ambrosio–Kirchheim normal currents. Our result holds in Polish spaces, or more generally in complete metric spaces for 1-currents with tight support.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113913"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Aw–Rascle–Zhang traffic models with nonlocal look-ahead interactions","authors":"Thomas Hamori ,&nbsp;Changhui Tan","doi":"10.1016/j.na.2025.113930","DOIUrl":"10.1016/j.na.2025.113930","url":null,"abstract":"<div><div>We present a new family of second-order traffic flow models, extending the Aw–Rascle–Zhang (ARZ) model to incorporate nonlocal interactions. Our model includes a specific nonlocal Arrhenius-type look-ahead slowdown factor. We establish both local and global well-posedness theories for these nonlocal ARZ models.</div><div>In contrast to the local ARZ model, where generic smooth initial data typically lead to finite-time shock formation, we show that our nonlocal ARZ model exhibits global regularity for a class of smooth subcritical initial data. Our result highlights the potential of nonlocal interactions to mitigate shock formations in second-order traffic flow models.</div><div>Our analytical approach relies on investigating phase plane dynamics. We introduce a novel comparison principle based on a mediant inequality to effectively handle the nonlocal information inherent in our model.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113930"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some results on g-stability for hypersurfaces in an initial data set","authors":"A.B. Lima ,&nbsp;R.M. Batista ,&nbsp;P.A. Sousa","doi":"10.1016/j.na.2025.113914","DOIUrl":"10.1016/j.na.2025.113914","url":null,"abstract":"<div><div>We study the <span><math><mi>g</mi></math></span>-stability of hypersurfaces <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math></span> with null expansion <span><math><mrow><msup><mrow><mi>θ</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mi>h</mi><mo>≥</mo><mn>0</mn></mrow></math></span> in an <span><math><mi>n</mi></math></span>-dimensional initial data set <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> with cosmological constant <span><math><mi>Λ</mi></math></span>. First, under natural energy conditions, we demonstrate that <span><math><mrow><msup><mrow><mi>Σ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>⊂</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> admits a metric with positive scalar curvature. Second, for a <span><math><mi>g</mi></math></span>-stable surface <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> of genus <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>Σ</mi><mo>)</mo></mrow></mrow></math></span>, we establish an inequality relating the area of <span><math><mi>Σ</mi></math></span>, its genus, <span><math><mi>Λ</mi></math></span>, and the charge <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>Σ</mi><mo>)</mo></mrow></mrow></math></span>. Moreover, if equality holds and <span><math><mrow><mi>Λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is a round 2-sphere. Finally, for a <span><math><mi>g</mi></math></span>-stable, two-sided, closed hypersurface <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> in a 5-dimensional initial data set <span><math><msup><mrow><mi>M</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span> satisfying natural energy conditions, we derive an inequality involving the area of <span><math><mi>Σ</mi></math></span>, its charge <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>Σ</mi><mo>)</mo></mrow></mrow></math></span>, and a positive constant depending on the total traceless Ricci curvature of <span><math><mi>Σ</mi></math></span>. Equality implies that <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> is isometric to <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113914"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On dimension-free and potential-free estimates for Riesz transforms associated with Schrödinger operators","authors":"Jacek Dziubański","doi":"10.1016/j.na.2025.113918","DOIUrl":"10.1016/j.na.2025.113918","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>L</mi><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> be a Schrödinger operator on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, where <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>V</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. We give a short proof of dimension free <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-estimates, <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, for the vector of the Riesz transforms <span><math><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>,</mo><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>,</mo><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math></span> The constant in the estimates does not depend on the potential <span><math><mi>V</mi></math></span>. We simultaneously provide a short proof of the weak-type <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> estimates for <span><math><mrow><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113918"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144842243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Higher order expansion at infinity of solutions for Monge–Ampère equations in the half space","authors":"Lichun Liang","doi":"10.1016/j.na.2025.113912","DOIUrl":"10.1016/j.na.2025.113912","url":null,"abstract":"<div><div>In this paper, we investigate the asymptotic behavior of viscosity solutions for Monge–Ampère equations in the half space with a Dirichlet boundary condition on the flat boundary. Via the Kelvin transform, we characterize the asymptotic remainders by a single function near the origin. Such a function is smooth in the neighborhood of the origin in even dimension, but only <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> <span><math><mrow><mo>(</mo><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn><mo>)</mo></mrow></math></span> in odd dimension.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113912"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of positive radial steady states for the parabolic Hénon–Lane–Emden system","authors":"Daniel Devine ,&nbsp;Paschalis Karageorgis","doi":"10.1016/j.na.2025.113945","DOIUrl":"10.1016/j.na.2025.113945","url":null,"abstract":"<div><div>When it comes to the nonlinear heat equation <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span>, the stability of positive radial steady states in the supercritical case was established in the classical paper by Gui, Ni and Wang. We extend this result to systems of reaction–diffusion equations by studying the positive radial steady states of the parabolic Hénon–Lane–Emden system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi></mtd><mtd><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>k</mi></mrow></msup><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup></mtd><mtd><mtext>in</mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>v</mi></mtd><mtd><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mi>l</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></mtd><mtd><mtext>in</mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>k</mi><mo>,</mo><mi>l</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>p</mi><mi>q</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>. Assume that <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span> lies either on or above the Joseph–Lundgren critical curve which arose in the work of Chen, Dupaigne and Ghergu. Then all positive radial steady states have the same asymptotic behavior at infinity, and they are all stable solutions of the parabolic Hénon–Lane–Emden system in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113945"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}