Existence and multiplicity of solutions for critical nonlocal equations with variable exponents

Abstract

ABSTRACT In this paper, we are interested in a class of critical nonlocal problems with variable exponents of the form: where M is the Kirchhoff function, λ is a real parameter and f is a continuous function. We also assume that , where is the critical Sobolev exponent for variable exponents. The strategy of the proof for these results is to approach the problem variationally by using the mountain pass theorem and the concentration-compactness principles for fractional Sobolev spaces with variable exponents. In addition, we obtain the existence and multiplicity of nontrivial solutions for the above problem in non-degenerate and degenerate cases.