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.