Results 21 to 30 of about 200 (141)
(N,q)$(N,q)$‐Laplacian equations with one‐sided critical exponential growth
Mathematische Nachrichten, Volume 299, Issue 3, Page 675-698, March 2026.Abstract We prove the existence of two non‐trivial weak solutions for a class of quasilinear, non‐homogeneous elliptic problems driven by the (N,q)$(N,q)$‐Laplacian with one‐sided critical exponential growth in a bounded domain Ω⊂RN$\Omega \subset \mathbb {R}^{N}$. The first solution is obtained as a local minimizer of the associated energy functional;
Elisandra Gloss +2 more
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Infinitely many homoclinic solutions for a class of damped vibration problems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{
Huijuan Xu, Shan Jiang, Guanggang Liu
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Numerical Study of a Nonlocal Nonlinear Schrödinger Equation (MMT Model)
Studies in Applied Mathematics, Volume 156, Issue 3, March 2026.ABSTRACT In this paper, we study a nonlocal nonlinear Schrödinger equation (MMT model). We investigate the effect of the nonlocal operator appearing in the nonlinearity on the long‐term behavior of solutions, and we identify the conditions under which the solutions of the Cauchy problem associated with this equation are bounded globally in time in the ...
Amin Esfahani, Gulcin M. Muslu
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Curve-straightening and the Palais-Smale condition [PDF]
Transactions of the American Mathematical Society, 1998 This paper considers the negative gradient trajectories associated with the modified total squared curvature functional ∫
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Fractional Q$Q$‐curvature on the sphere and optimal partitions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara +2 more
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Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type
Abstract and Applied Analysis, 2011 This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff type −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω.
Bitao Cheng, Xian Wu, Jun Liu
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Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang +3 more
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Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian
Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.Abstract In this paper, we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic p$p$‐Laplacian. The critical exponent is the usual p★$p^{\star }$ such that the embedding W01,p(Ω)⊂Lp★(Ω)$W^{1,p}_{0}(\Omega) \subset L^{p^{\star }}(\Omega)$ is not compact.
Stefano Biagi +3 more
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Ume's u-distance and its relation with both (PS)-condition and coercivity
Electronic Journal of Differential Equations, 2011 In this article, we study the connection between the u-distance and a new Palais-Smale condition of compactness. We compare this Palais-Smale condition with the coercivity.
Georgiana Goga
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
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