Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well

Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.

Original languageEnglish
Pages (from-to)413-439
Number of pages27
JournalCalculus of Variations and Partial Differential Equations
Volume53
Issue number1-2
DOIs
Publication statusPublished - 2015 Jan 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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