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(p, q)-Equations with Negative Concave Terms

Crespo-Blanco, Ángel; Papageorgiou, Nikolaos S.; Winkert, Patrick

In this paper, we study a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction that has the combined effects of a negative concave term and of an asymmetric perturbation which is superlinear on the positive semiaxis and resonant in the negative one. We prove a multiplicity theorem for such problems obtaining three nontrivial solutions, all with sign information. Furthermore, under a local symmetry condition, we prove the existence of a whole sequence of sign-changing solutions converging to zero in C10(Ω¯¯¯¯).
Published in: The journal of geometric analysis, 10.1007/s12220-022-01044-5, Springer Nature