Existence and multiple solutions for the critical fractional p‐Kirchhoff type problems involving sign‐changing weight functions

Abstract

The aim of this paper is to study the existence and multiplicity of nonnegative solutions for the following critical Kirchhoff equation involving the fractional p‐Laplace operator . More precisely, we consider where is an open bounded domain with Lipschitz boundary with m > 1, a > 0, b > 0, dimension is the fractional critical Sobolev exponent, and the parameters λ > 0, 0 < s < 1 < q < p < ∞. Applying the Nehari manifold, fibering maps and Krasnoselskii genus theory, we investigate the existence and multiplicity of nonnegative solutions.