On fractional p(⋅)-Schrödinger-Kirchhoff equations with the critical exponent in RN

Abstract

In the present paper, we discuss a class of critical Schrödinger-Kirchhoff type problem involving the fractional $p(\cdot )$-Laplacian. Firstly, for the critical case, we analyze the loss of compactness of the problem using the famous concentration-compactness principles. Next, the existence of nontrivial solutions is derived by utilizing the Nehari manifold approach. Finally, a simple example is given to show the validity of our main theorem's conditions. Our study improves and extends some recent work in the literature.