On a class of p(x)-Choquard equations with sign-changing potential and upper critical growth

Abstract

Motived by the Hardy–Littlewood–Sobolev inequality for variable exponents, in this paper we use variational methods to prove the existence of a weak solution for a class of p(x)-Choquard equations with upper critical growth. Using truncation arguments and Krasnoselskii’s genus, we also show a multiplicity of solutions for a class of p(x)-Choquard equations with a nonlocal and non-degenerate Kirchhoff term. Also we show that the solutions obtained belong to $$L^{\infty }({\mathbb {R}}^{N})$$ and have polynomial decay.