Ground state and multiple solutions via generalized Nehari manifold

DOI10.1016/j.na.2014.02.018zbMath1316.35106OpenAlexW2084200590MaRDI QIDQ2443045

Wen Ming Zou, Xue Xiu Zhong

Publication date: 4 April 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.02.018

zbMATH Keywords

variational methodsground stateSchrödinger equationsperiodic domaingeneralized Nehari manifoldstrongly indefinite

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20)

Related Items (8)

Multiple entire solutions of fractional Laplacian Schrödinger equations ⋮ Ground state solution for strongly indefinite Choquard system ⋮ Generalized Nehari manifold and semilinear Schrödinger equation with weak monotonicity condition on the nonlinear term ⋮ Multiplicity of solutions for Schrödinger equations with concave-convex nonlinearities ⋮ Ground state sign-changing solutions for a class of Schrödinger-Poisson type problems in \({\mathbb{R}^{3}}\) ⋮ Non-Nehari manifold method for asymptotically periodic Schrödinger equations ⋮ Radial ground state sign-changing solutions for a class of asymptotically cubic or super-cubic Schrödinger-Poisson type problems ⋮ Ground state solutions and periodic solutions with minimal periods to second-order Hamiltonian systems

Cites Work

• On superlinear Schrödinger equations with periodic potential
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Ground state solutions for some indefinite variational problems
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• Generalized linking theorem with an application to a semilinear Schrödinger equation
• Standing wave solutions of the nonlinear Schrödinger equation in \(\mathbb R^N\)
• Multi-bump solutions for a strongly indefinite semilinear Schrödinger equation without symmetry or convexity assumptions
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