Existence of weak solutions for a double phase variable exponent problem with a gradient dependent reaction term

In the present paper, we study the existence of at least one weak solution for a class of double phase variable exponent problem with a reaction term depending on the gradient and on two real parameters. By using the topological degree theory for a class of demicontinuous operators of generalized (S+) and the theory of the variable exponent Sobolev spaces, we obtain the existence of at least one weak solution of this problem.