Results 21 to 30 of about 2,592,777 (103)
Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 13324-13360, August 2026.ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
wiley +1 more source
Low eigenvalues of the p$p$–Laplacian in general open sets
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We consider the minmax Ljusternik–Schnirelmann levels of the constrained p$p$–Dirichlet integral on a general open set of the Euclidean space. We show that, whenever one of these levels lies below the threshold given by the Lp$L^p$ Poincaré constant “at infinity,” it actually defines an eigenvalue of the Dirichlet p$p$–Laplacian. We also prove
Lorenzo Brasco +2 more
wiley +1 more source
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media
Boundary Value Problems, 2005 We study nonlinear eigenvalue problems of the type −div(a(x)∇u)=g(λ,x,u) in â„ÂN, where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity ...
Vicenţiu RăDulescu +1 more
doaj +2 more sources
, 2002 Dans cette Note, nous proposons une nouvelle preuve de l'existence d'un minimum pour les méthodes de multiconfiguration en Chimie Quantique. Nous utilisons une propriété de Palais–Smale (avec information de type Morse), dont la démonstration repose sur ...
Lewin, Mathieu
core +2 more sources
Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem [PDF]
Opuscula Mathematica, 2015 We consider a nonlinear Neumann elliptic equation driven by a \(p\)-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that
Liliana Klimczak
doaj +1 more source
(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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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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A Variant of Clark\u27s Theorem and its Applications for Nonsmooth Functionals Without the Palais-Smale Condition [PDF]
, 2017 By introducing a new notion of the genus with respect to the weak topology in Banach spaces, we prove a variant of Clark\u27s theorem for nonsmooth functionals without the Palais-Smale condition.
Zhi-Qiang Wang +5 more
core +1 more source
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
wiley +1 more source
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
wiley +1 more source