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

Silvia Cingolani, Louis Jeanjean, Kazunaga Tanaka

研究成果: Article査読

12 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)413-439
ページ数27
ジャーナルCalculus of Variations and Partial Differential Equations
53
1-2
DOI
出版ステータスPublished - 2015 5

ASJC Scopus subject areas

  • 分析
  • 応用数学

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