Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 75, pp. 1-16.

Title: Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance

Authors: Silvia Frassu (Univ. of Cagliari, Italy)
         Eugenio M. Rocha (Univ. of Aveiro, Portugal)
         Vasile Staicu (Univ. of Aveiro, Portugal)

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 Holder versus Sobolev minimizers relation play an important role.


Submitted April 3, 2019. Published May 31, 2019.
Math Subject Classifications: 47G20, 35R11, 34A60, 49J92, 58E05.
Key Words: Integrodifferential operators; differential inclusions,
           nonsmooth analysis; critical point theory.