Existence and asymptotic behavior of positive solutions for a class of locally superlinear Schrödinger equation

Shinji Adachi, Norihisa Ikoma, Tatsuya Watanabe

Research output: Contribution to journalArticlepeer-review

Abstract

This paper treats the existence of positive solutions of - Δ u+ V(x) u= λ f(u) in RN. Here N≥ 1 , λ > 0 is a parameter and f(u) satisfies conditions only in a neighborhood of u= 0. We shall show the existence of positive solutions with potential of trapping type or G-symmetric potential where G⊂ O(N). Our results extend previous results (Adachi and Watanabe in J Math Anal Appl 507:125765, 2022; Costa and Wang in Proc Am Math Soc 133(3):787–794, 2005; do Ó et al. in J Math Anal Appl 342:432–445, 2008) as well as we also study the asymptotic behavior of a family (uλ)λ≥λ0 of positive solutions as λ → ∞.

Original languageEnglish
JournalManuscripta Mathematica
DOIs
Publication statusAccepted/In press - 2022

ASJC Scopus subject areas

  • Mathematics(all)

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