Quasilinear nonlocal elliptic problems with varable singular exponent

Prashanta Garain*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this article, we provide existence results to the following nonlocal equation (Formula presented) where (Formula presented) is the fractional p-Laplacian operator. Here Ω ⊂ RN is a smooth bounded domain, s ∈ (0, 1), p > 1 and N > sp. We establish existence of at least one weak solution for (Pλ) when g(x, u) = f(x)u−q(x) and existence of at least two weak solutions when g(x, u) = λu−q(x) + ur for a suitable range of λ > 0. Here (Formula presented) where (Formula presented) is the critical Sobolev exponent and (Formula presented).

Original languageEnglish
Pages (from-to)5059-5075
Number of pages17
JournalCOMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume19
Issue number11
DOIs
Publication statusPublished - Nov 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional p-Laplacian
  • Multiple weak solutions
  • Singular nonlinearity
  • Variable exponent
  • Variational method

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