Nonlinear scalar field equations: existence of a positive solution with infinitely many bumps

DOI10.1016/j.anihpc.2013.08.008zbMath1311.35081OpenAlexW2040945946MaRDI QIDQ2259426

Donato Passaseo, Sergio Solimini, Giovanna Cerami

Publication date: 4 March 2015

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2013.08.008

zbMATH Keywords

variational methodsSchrödinger equationsolutions with infinitely many bumps

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20) Positive solutions to PDEs (35B09)

Related Items (15)

Infinitely many segregated vector solutions of Schrodinger system ⋮ Infinitely many positive solutions of nonlinear Schrödinger equations ⋮ Multiplicity results for critical \(p\)-Laplacian problems ⋮ Generalized quasilinear elliptic equations in \(\mathbb{R}^N\) ⋮ Multiscale weak compactness in metric spaces ⋮ A positive bound state for an asymptotically linear or superlinear Schrödinger equation ⋮ The role of planar symmetry and of symmetry constraints in the proof of existence of solutions to some scalar field equations ⋮ Infinitely many positive solutions for nonlinear equations with non-symmetric potentials ⋮ Sign-changing solutions to a partially periodic nonlinear Schrödinger equation in domains with unbounded boundary ⋮ Infinitely many positive solutions of fractional nonlinear Schrödinger equations with non-symmetric potentials ⋮ Multiplicity of solutions of nonlinear scalar field equations ⋮ Variational properties of the first curve of the Fučík spectrum for elliptic operators ⋮ Infinitely many solutions for a nonlinear Schrödinger equation with general nonlinearity ⋮ Infinitely many positive solutions for a class of semilinear elliptic equations ⋮ Existence and Multiplicity Results for Some Scalar Fields Equations

Cites Work

• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• On a min-max procedure for the existence of a positive solution for certain scalar field equations in \({\mathbb{R}}^ N\)
• Some nonlinear elliptic problems in unbounded domains
• On the existence of a positive solution of semilinear elliptic equations in unbounded domains
• Infinitely many bound states for some nonlinear scalar field equations
• Infinitely many positive solutions for the nonlinear Schrödinger equations in \(\mathbb R^N\)
• Infinitely Many Positive Solutions to Some Scalar Field Equations with Nonsymmetric Coefficients

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