(p, q)-Equations with Negative Concave Terms

Abstract In this paper, we study a nonlinear Dirichlet problem driven by the ( p , q )-Laplacian and with reaction that has combined effects of negative concave term an asymmetric perturbation which is superlinear on positive semiaxis resonant in one. We prove multiplicity theorem for such problems obtaining three nontrivial solutions, all sign information. Furthermore, under local symmetry condition, existence whole sequence sign-changing solutions converging to zero $$C^1_0(\overline{\Omega })$$ C 0 1 ( Ω ¯ ) .