Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Existence and nonexistence of solutions for weighted elliptic inequalities involving gradient terms","authors":"Roberta Filippucci ,&nbsp;Yadong Zheng","doi":"10.1016/j.na.2025.113951","DOIUrl":"10.1016/j.na.2025.113951","url":null,"abstract":"<div><div>In this paper we prove existence and nonexistence theorems for positive solutions of elliptic inequalities for general quasilinear operators, including <span><math><mi>m</mi></math></span>-Laplacian, mean curvature and generalized mean curvature operator, in the entire <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> with a reaction involving power type gradient terms and positive weights, possibly singular or degenerate. A complete picture for the exponents involved is given. The proof technique is based on cumbersome integral a priori estimates, in the spirit of the nonlinear capacity method. No maximum principle or growth conditions at infinity for the solutions are required.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113951"},"PeriodicalIF":1.3,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157795","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 existence of periodic solutions for damped asymmetric oscillators","authors":"Alessandro Fonda ,&nbsp;Giuliano Klun ,&nbsp;Andrea Sfecci","doi":"10.1016/j.na.2025.113946","DOIUrl":"10.1016/j.na.2025.113946","url":null,"abstract":"<div><div>We propose some new sufficient conditions for the existence of periodic solutions of an asymmetric oscillator with a positive damping term. Our results are complemented by an example where, in some situations, no periodic solutions may exist. This fact is well known in the undamped case, when the resonance phenomenon may appear. However, the damped case presents some unintuitive features which have not been so thoroughly studied in the literature, and the overall picture still has several aspects which need to be better understood.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113946"},"PeriodicalIF":1.3,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094803","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":"SBV functions in Carnot–Carathéodory spaces","authors":"Marco Di Marco ,&nbsp;Sebastiano Don ,&nbsp;Davide Vittone","doi":"10.1016/j.na.2025.113944","DOIUrl":"10.1016/j.na.2025.113944","url":null,"abstract":"<div><div>We introduce the space SBV<span><math><msub><mrow></mrow><mrow><mi>X</mi></mrow></msub></math></span> of special functions with bounded <span><math><mi>X</mi></math></span>-variation in Carnot–Carathéodory spaces and study its main properties. Our main outcome is an approximation result, with respect to the BV<span><math><msub><mrow></mrow><mrow><mi>X</mi></mrow></msub></math></span> topology, for SBV<span><math><msub><mrow></mrow><mrow><mi>X</mi></mrow></msub></math></span> functions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113944"},"PeriodicalIF":1.3,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094805","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":"2025-09-16","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 least energy solutions for a nonlinear Schrödinger system with K-wise interaction","authors":"Lorenzo Giaretto,&nbsp;Nicola Soave","doi":"10.1016/j.na.2025.113938","DOIUrl":"10.1016/j.na.2025.113938","url":null,"abstract":"<div><div>In this paper we establish existence and properties of minimal energy solutions for the weakly coupled system <span><span><span><math><mrow><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><mi>K</mi><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><mi>β</mi><mo>|</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><munder><mrow><mo>∏</mo></mrow><mrow><mi>j</mi><mo>≠</mo><mi>i</mi></mrow></munder><mo>|</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>j</mi></mrow></msub><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup><mspace></mspace><mspace></mspace><mtext>in</mtext><mspace></mspace><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mspace></mspace></mtd></mtr><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><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></mrow><mo>,</mo><mspace></mspace></mtd></mtr></mtable></mrow></mfenced><mspace></mspace><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>K</mi><mo>,</mo></mrow></math></span></span></span>characterized by <span><math><mi>K</mi></math></span>-wise interaction (namely the interaction term involves the product of all the components). We consider both attractive (<span><math><mrow><mi>β</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>) and repulsive cases (<span><math><mrow><mi>β</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>), and we give sufficient conditions on <span><math><mi>β</mi></math></span> in order to have least energy fully non-trivial solutions, if necessary under a radial constraint. We also study the asymptotic behaviour of least energy fully non-trivial radial solutions in the limit of strong competition <span><math><mrow><mi>β</mi><mo>→</mo><mo>−</mo><mi>∞</mi></mrow></math></span>, showing partial segregation phenomena which differ substantially from those arising in pairwise interaction models.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113938"},"PeriodicalIF":1.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048354","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":"Minimization of the first positive eigenvalue for the beam equation with indefinite weight","authors":"Yu Gan ,&nbsp;Zhaowen Zheng ,&nbsp;Kun Li ,&nbsp;Jing Shao","doi":"10.1016/j.na.2025.113933","DOIUrl":"10.1016/j.na.2025.113933","url":null,"abstract":"<div><div>In this paper, we obtain the sharp estimate of the first positive eigenvalue for the beam equation <span><span><span><math><mrow><msup><mrow><mi>y</mi></mrow><mrow><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>λ</mi><mi>m</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span></span></span>with Lidstone boundary condition, where weight function <span><math><mi>m</mi></math></span> is allowed to change sign. We first establish a variational characterization for the first positive eigenvalue of the measure differential equation (MDE) <span><span><span><math><mrow><mi>d</mi><msup><mrow><mi>y</mi></mrow><mrow><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>λ</mi><mi>y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>d</mi><mi>μ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>and solve the corresponding minimization problem of the first positive eigenvalue for the MDE, where <span><math><mi>μ</mi></math></span> is a suitable measure. Then by finding the relationship between minimization problem for the first positive eigenvalue of ordinary differential equation (ODE) and that of MDE, we obtain the explicit sharp lower bound of the first positive eigenvalue for the indefinite beam equation.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113933"},"PeriodicalIF":1.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048352","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":"Interior and boundary regularity of mixed local nonlocal problem with singular data and its applications","authors":"R. Dhanya ,&nbsp;Jacques Giacomoni ,&nbsp;Ritabrata Jana","doi":"10.1016/j.na.2025.113940","DOIUrl":"10.1016/j.na.2025.113940","url":null,"abstract":"<div><div>In this article, we examine the Hölder regularity of solutions to equations involving a mixed local-nonlocal nonlinear nonhomogeneous operator <span><math><mrow><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>+</mo><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>q</mi></mrow><mrow><mi>s</mi></mrow></msubsup></mrow></math></span> with singular data, under the minimal assumption that <span><math><mrow><mi>p</mi><mo>&gt;</mo><mi>s</mi><mi>q</mi></mrow></math></span>. The regularity result is twofold: we establish interior gradient Hölder regularity for locally bounded data and boundary regularity for singular data. We prove both boundary Hölder and boundary gradient Hölder regularity depending on the degree of singularity. Additionally, we establish a strong comparison principle for this class of problems, which holds independent significance. As the applications of these qualitative results, we further study sublinear and subcritical perturbations of singular nonlinearity.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113940"},"PeriodicalIF":1.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048353","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":"Three dimensional stationary solutions of the Electron MHD equations","authors":"Qirui Peng","doi":"10.1016/j.na.2025.113935","DOIUrl":"10.1016/j.na.2025.113935","url":null,"abstract":"<div><div>The goal of this paper is to construct non-trivial steady-state weak solutions of the three dimensional Electron Magnetohydrodynamics equations in the class of <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> for some small <span><math><mrow><mi>s</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. By exploiting the formulation of the stationary EMHD equations one can treat them as generalized Navier–Stokes equations with half Laplacian. Therefore with convex integration scheme we obtained such stationary weak solutions, which is not yet realizable in the case of classical 3D Navier–Stokes equations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113935"},"PeriodicalIF":1.3,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019143","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":"A singular double phase eigenvalue problem with a superlinear indefinite perturbation","authors":"Jiangfeng Han ,&nbsp;Zhenhai Liu ,&nbsp;Nikolaos S. Papageorgiou","doi":"10.1016/j.na.2025.113941","DOIUrl":"10.1016/j.na.2025.113941","url":null,"abstract":"<div><div>We consider a Dirichlet problem driven by a double phase differential operator and a reaction which exhibits the combined effects of a parametric singular term and of an indefinite superlinear perturbation. The superlinearity condition on the perturbation is very general. Using variational tools, truncation and comparison techniques and critical groups, we prove an existence and multiplicity result which is global in the parameter (bifurcation-type result).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113941"},"PeriodicalIF":1.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010445","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":"Dirac delta as a generalized holomorphic function","authors":"Sekar Nugraheni ,&nbsp;Paolo Giordano","doi":"10.1016/j.na.2025.113921","DOIUrl":"10.1016/j.na.2025.113921","url":null,"abstract":"<div><div>The definition of a non-trivial space of generalized functions of a complex variable allowing to consider derivatives of continuous functions is a non-obvious task, e.g. because of Morera theorem, because distributional Cauchy–Riemann equations implies holomorphicity and of course because including Dirac delta seems incompatible with the identity theorem. Surprisingly, these results can be achieved if we consider a suitable non-Archimedean extension of the complex field, i.e. a ring where infinitesimal and infinite numbers return to be available. In this first paper, we set the definition of generalized holomorphic function and prove the extension of several classical theorems, such as Cauchy–Riemann equations, Goursat, Looman–Menchoff and Montel theorems, generalized complex differentiability implies smoothness, embedding of distributions, closure with respect to composition and hence non-linear operations on these generalized functions. The theory hence addresses several limitations of Colombeau theory of generalized holomorphic functions. The final aim of this series of papers is to prove the Cauchy–Kowalevski theorem including also distributional PDE or singular boundary conditions and nonlinear operations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113921"},"PeriodicalIF":1.3,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988178","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}