Multiple solutions for Kirchhoff–Schrödinger problems of fractional p-Laplacian involving Sobolev–Hardy critical exponent

Abstract

ABSTRACT This paper is devoted to multiple solutions to a Kirchhoff–Schrödinger type problem of fractional p-Laplacian involving the Sobolev–Hardy critical exponent and a parameter 0 $ ]]> λ > 0 . With some suitable assumptions on the potential V ( x ) and the nonlinearity f ( x , u ) , the Krasnoselskii's genus argument is exploited to show the existence of infinitely many solutions if λ is sufficiently large. Furthermore, we employ a fractional version of the concentration-compactness to prove that there are m-pairs solutions of the problem provided that λ is small enough and the nonlinear force f ( x , ⋅ ) is odd.