Electron. J. Differential Equations,
Vol. 2019 (2019), No. 75, pp. 1-16.
Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance
Silvia Frassu, Eugenio M. Rocha, Vasile Staicu
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.
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Silvia Frassu
Department of Mathematics and Computer Science
University of Cagliari
Viale L. Merello 92
09123 Cagliari, Italy
email: silvia.frassu@gmail.com
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Eugénio M. Rocha
CIDMA - Center for Research and Development in Mathematics and Applications
Department of Mathematics
University of Aveiro
3810-193 Aveiro, Portugal
email: eugenio@ua.pt
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Vasile Staicu
CIDMA - Center for Research and Development in Mathematics and Applications
Department of Mathematics
University of Aveiro
3810-193 Aveiro, Portugal
email: vasile@ua.pt
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