Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Optimal planar immersions of prescribed winding number and Arnold invariants","authors":"Anna Lagemann,&nbsp;Heiko von der Mosel","doi":"10.1016/j.na.2025.113942","DOIUrl":"10.1016/j.na.2025.113942","url":null,"abstract":"<div><div>Vladimir Arnold defined three invariants for generic planar immersions, i.e. planar curves whose self-intersections are all transverse double points. We use a variational approach to study these invariants by investigating a suitably truncated knot energy, the tangent-point energy. We prove existence of energy minimizers for each truncation parameter <span><math><mrow><mi>δ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> in a class of immersions with prescribed winding number and Arnold invariants, and establish Gamma convergence of the truncated tangent-point energies to a limiting renormalized tangent-point energy as <span><math><mrow><mi>δ</mi><mo>→</mo><mn>0</mn></mrow></math></span>. Moreover, we show that any sequence of minimizers subconverges in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, and the corresponding limit curve has the same topological invariants, self-intersects exclusively at right angles, and minimizes the renormalized tangent-point energy among all curves with right self-intersection angles. In addition, the limit curve is an almost-minimizer for all of the original truncated tangent-point energies as long as the truncation parameter <span><math><mi>δ</mi></math></span> is sufficiently small. Therefore, this limit curve serves as an “optimal” curve in the class of generic planar immersions with prescribed winding number and Arnold invariants.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"263 ","pages":"Article 113942"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270052","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":"Behavior of absorbing and generating p-Robin eigenvalues in bounded and exterior domains","authors":"Lukas Bundrock,&nbsp;Tiziana Giorgi,&nbsp;Robert Smits","doi":"10.1016/j.na.2025.113943","DOIUrl":"10.1016/j.na.2025.113943","url":null,"abstract":"<div><div>We establish rigorous quantitative inequalities for the first eigenvalue of the generalized <span><math><mi>p</mi></math></span>-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter <span><math><mi>α</mi></math></span> is positive, and the superconducting generation regime (<span><math><mrow><mi>α</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>), where the boundary acts as a source. In bounded domains, we use a unified approach to derive a precise asymptotic behavior for all <span><math><mi>p</mi></math></span> and all small real <span><math><mi>α</mi></math></span>, improving existing results in various directions, including requiring weaker boundary regularity for the case of the classical 2-Robin problem, studied in the fundamental work by René Sperb. In exterior domains, we characterize the existence of eigenvalues, establish general inequalities and asymptotics as <span><math><mrow><mi>α</mi><mo>→</mo><mn>0</mn></mrow></math></span> for the first eigenvalue of the exterior of a ball, and obtain some sharp geometric inequalities for convex domains in two dimensions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113943"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157798","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 boundedness for solutions of a class of non-uniformly elliptic anisotropic problems","authors":"Stefano Biagi ,&nbsp;Giovanni Cupini ,&nbsp;Elvira Mascolo","doi":"10.1016/j.na.2025.113915","DOIUrl":"10.1016/j.na.2025.113915","url":null,"abstract":"<div><div>We consider a class of energy integrals, associated to nonlinear and non-uniformly elliptic equations, with integrands <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow></mrow></math></span> satisfying anisotropic <span><math><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>q</mi></mrow></math></span>-growth conditions of the form <span><math><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mrow><mo>|</mo><msub><mrow><mi>ξ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo></mrow></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msup><mo>≤</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow><mo>≤</mo><mi>μ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mfenced><mrow><msup><mrow><mrow><mo>|</mo><mi>ξ</mi><mo>|</mo></mrow></mrow><mrow><mi>q</mi></mrow></msup><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>γ</mi></mrow></msup><mo>+</mo><mn>1</mn></mrow></mfenced></mrow></math></span> for some exponents <span><math><mrow><mi>γ</mi><mo>≥</mo><mi>q</mi><mo>≥</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, and non-negative functions <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>μ</mi></mrow></math></span> subject to suitable summability assumptions. We prove the local boundedness of scalar local quasi-minimizers of such integrals.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113915"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988180","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":"2026-01-01","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":"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":"2026-01-01","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":"Hopf’s lemmas and boundary behavior of solutions to the fractional Laplacian in Orlicz-Sobolev spaces","authors":"Pablo Ochoa ,&nbsp;Ariel Salort","doi":"10.1016/j.na.2025.113923","DOIUrl":"10.1016/j.na.2025.113923","url":null,"abstract":"<div><div>In this article we study different extensions of the celebrated Hopf’s boundary lemma within the context of a family of nonlocal, nonlinear and nonstandard growth operators. More precisely, we examine the behavior of solutions of the fractional <span><math><mi>a</mi></math></span>-Laplacian operator near the boundary of a domain satisfying the interior ball condition. Our approach addresses problems involving both constant-sign and sign-changing potentials.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113923"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865185","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":"Eigenvalues of nonlinear (p,q)-fractional Laplace operator under nonlocal Neumann conditions","authors":"Pierre Aime Feulefack ,&nbsp;Emmanuel Wend-Benedo Zongo","doi":"10.1016/j.na.2025.113949","DOIUrl":"10.1016/j.na.2025.113949","url":null,"abstract":"<div><div>In this paper, we investigate on a bounded open set of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> with smooth boundary, an eigenvalue problem involving a sum of nonlocal operators <span><math><mrow><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>p</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>+</mo><msubsup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>q</mi></mrow><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msubsup></mrow></math></span> with <span><math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> and subject to the corresponding homogeneous nonlocal <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Neumann boundary condition. A careful analysis of the considered problem leads us to a complete description of the set of eigenvalues as being the precise interval <span><math><mrow><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>∪</mo><mrow><mo>(</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>q</mi><mo>)</mo></mrow><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> is the first nonzero eigenvalue of the homogeneous fractional <span><math><mi>q</mi></math></span>-Laplacian under nonlocal <span><math><mi>q</mi></math></span>-Neumann boundary condition. Due to the nonlocal feature of the operators appearing in the equations, some purely nonlocal situations occur and bring in a difference in the study of nonlocal problems compared to local ones. Furthermore, we establish that every eigenfunctions is globally bounded.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113949"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157796","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":"Convergence of normalizations for partially integrable differential systems","authors":"Wenyong Huang ,&nbsp;Valery G. Romanovski ,&nbsp;Xiang Zhang","doi":"10.1016/j.na.2025.113902","DOIUrl":"10.1016/j.na.2025.113902","url":null,"abstract":"<div><div>This paper provides some criteria to characterize convergence of normalizations which transform partially integrable analytic differential systems to their Poincaré–Dulac normal forms. For a family of four-dimensional partially integrable differential systems near an equilibrium which has one pair of conjugate imaginary eigenvalues and a pair of resonant nonzero real eigenvalues, we prove convergence of their normalizations. For analytic differential systems with dimension larger than 4, we illustrate that partial integrability may not be sufficient to ensure convergence of the normalizations even though Bruno’s condition <span><math><mi>ω</mi></math></span> holds. This work generalizes in a natural way the classical results by Poincaré and Lyapunov for a monodromic equilibrium, as well as the one by Moser for a hyperbolic saddle of analytic Hamiltonian systems of one degree of freedom.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113902"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779749","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":"Ideal magnetohydrodynamics around couette flow: Long time stability and vorticity–current instability","authors":"Niklas Knobel","doi":"10.1016/j.na.2025.113937","DOIUrl":"10.1016/j.na.2025.113937","url":null,"abstract":"<div><div>This article considers the ideal 2D magnetohydrodynamic equations in a infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constant magnetic field. This incorporates important physical effects, including mixing and coupling of velocity and magnetic field. We establish the existence and stability of the velocity and magnetic field for Gevrey-class perturbations of size <span><math><mi>ɛ</mi></math></span>, valid up to times <span><math><mrow><mi>t</mi><mo>∼</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. Additionally, the vorticity and current grow as <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> and there is no inviscid damping of the velocity and magnetic field. This is similar to the above threshold case for the <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> Navier–Stokes (Jacob Bedrossian et al., 2022) where growth in ‘streaks’ leads to time scales of <span><math><mrow><mi>t</mi><mo>∼</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>. In particular, for the ideal MHD equations, our article suggests that for a wide range of initial data, the scenario “induction by shear <span><math><mo>⇒</mo></math></span> vorticity and current growth <span><math><mo>⇒</mo></math></span> vorticity and current breakdown” leads to instability and possible turbulences.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113937"},"PeriodicalIF":1.3,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932827","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":"2026-01-01","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}