Infinitely many solutions for the fractional $p$&$q$ problem with critical Sobolev-Hardy exponents and sign-changing weight functions

Abstract

In this paper, we study the Kirchhoff type problems involving fractional $p$&$q$ problem with critical Sobolev-Hardy exponents and sign-changing weight functions. By using the fractional version of concentration-compactness principle together with Krasnoselskii's genus, we obtain the multiplicity of solutions for this kind problem. The main feature and difficulty of our equations arise in the fact that the Kirchhoff term $M$ could vanish at zero, that is, the problem is degenerate.