High perturbations of Choquard equations with critical reaction and variable growth

Abstract

This paper deals with the mathematical analysis of solutions for a new class of Choquard equations. The main features of the problem studied in this paper are the following: (i) the equation is driven by a differential operator with variable exponent; (ii) the Choquard term contains a nonstandard potential with double variable growth; and (iii) the lack of compactness of the reaction, which is generated by a critical nonlinearity. The main result establishes the existence of infinitely many solutions in the case of high perturbations of the source term. The proof combines variational and analytic methods, including the Hardy-Littlewood-Sobolev inequality for variable exponents and the concentration-compactness principle for problems with variable growth.