On the existence of positive solutions to a certain class of semilinear elliptic equations

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Abstract

In this paper, we study the following semilinear elliptic equation Δu=φ(V(x)u-f(x,u(x)))inRN,u∈H1(RN)where N≥ 1 and φ(s) , V(x), f(x, s) are given functions. Under some conditions on φ(s) , V(x) , f(x, s) , we show the existence of positive solution. In particular, we extend the result of Felmer and Ikoma (J Funct Anal 275(8):2162–2196, 2018). In Felmer and Ikoma (J Funct Anal 275(8):2162–2196, 2018), the existence of positive solution was proved by topological degree theoretic argument. In this paper, we employ the variational method.

Original languageEnglish
Article number28
JournalPartial Differential Equations and Applications
Volume2
Issue number2
DOIs
Publication statusPublished - 2021 Apr

Keywords

  • Concentration-compactness lemma
  • Mountain pass theorem
  • Positive solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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