Existence and multiplicity results for p(⋅)&q(⋅) fractional Choquard problems with variable order

Abstract

This paper is concerned with the existence and multiplicity of solutions for the fractional variable order Choquard type problem where and are two fractional Laplace operators with variable order and with different variable exponents and . Here is a bounded smooth domain with at least , λ is a real parameter, β, μ and k are continuous variable parameters, while F is the primitive function of a suitable f. Under some appropriate conditions on β and k, through variational methods, we prove existence and multiplicity of solutions for the above problem.