Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance
Rocha, Eugenio M.
Texas State University, Department of Mathematics
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.
Integrodifferential operators, Differential inclusions, Nonsmooth analysis, Critical point theory
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.