Quasilinear nonlocal elliptic problems with varable singular exponent

Prashanta Garain, Tuhina Mukherjee

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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
Issue number11
StatePublished - 1 Nov 2020
Externally publishedYes


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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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