Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance

Date

2019-05-31

Authors

Frassu, Silvia
Rocha, Eugenio M.
Staicu, Vasile

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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.

Description

Keywords

Integrodifferential operators, Differential inclusions, Nonsmooth analysis, Critical point theory

Citation

Frassu, S., Rocha, E. M., & Staicu, V. (2019). Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance. <i>Electronic Journal of Differential Equations, 2019</i>(75), pp. 1-16.

Rights

Attribution 4.0 International

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