Multiple solutions to logarithmic double phase problems involving superlinear nonlinearities

Abstract

This paper investigates a class of problems involving a logarithmic double phase operator with variable exponents and right-hand sides that consist of nonlinearities exhibiting subcritical and superlinear growth. Under very general assumptions, we prove the existence of at least two nontrivial bounded weak solutions for such problems whereby the solutions have opposite energy sign. In addition, we give conditions on the nonlinearity under which the solutions turn out to be nonnegative.