Locating peaks of a Schrödinger equation with sign-changing nonlinearity

DOI10.1016/J.NA.2010.09.062zbMath1205.35286OpenAlexW2031140714MaRDI QIDQ622393

Jianfu Yang, Andrés I. Ávila

Publication date: 31 January 2011

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.2010.09.062

zbMATH Keywords

energy functionalSchrödinger equationspike solutions

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) NLS equations (nonlinear Schrödinger equations) (35Q55) Positive solutions to PDEs (35B09)

Cites Work

• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
• On a class of nonlinear Schrödinger equations
• On concentration of positive bound states of nonlinear Schrödinger equations
• Solutions of elliptic equations with indefinite nonlinearities via Morse theory and linking
• Minimax theorems
• Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
• Dual variational methods in critical point theory and applications
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On Concentration of Positive Bound States of Nonlinear Schrödinger Equations with Competing Potential Functions
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
• Existence of positive solutions for a class of indefinite elliptic problems in \(\mathbb{R}^N\)

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