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The Dirichlet boundary value problem for elliptic equations involving the (p(x), q(x))-Laplacian operator with a reaction term depending on the gradient and on two real parameters is considered in this paper. Using the topological degree theory for a class of demicontinuous operators of generalized (S+) and the theory of the variable exponent Sobolev spaces, we prove the existence of at least one weak solution of such problem. [ABSTRACT FROM AUTHOR]