Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance

Frassu S.;Rocha E. M.;Staicu V.

2019-01-01

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Abstract

In this article, we study a pseudo-differential inclusion driven by a nonlocal anisotropic operator and a Clarke generalized subdifferential of a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. We prove the existence of three nontrivial solutions: one positive, one negative and one of unknown sign, using variational methods based on nosmooth critical point theory, more precisely applying the second deformation theorem and spectral theory. Here, a nosmooth anisotropic version of the Hölder versus Sobolev minimizers relation play an important role.