Double phase differential inclusion in Sobolev space with variable exponent

Abstract

In this paper, we examine a type of inclusion problem involving the two-phase operator, a discountious nonliearity and logarithmic perturbation.
Using the variational techniques combined with
we prove the existence of at least one weak solution within the framework of a Sobolev space with variable exponent. Our approach is variational, meaning the solution is identified as a critical point of the corresponding energy functional defined on the appropriate Sobolev space.