Electron. J. Differential Equations, Vol. 2018 (2018), No. 122, pp. 1-14.

Two solutions for fractional p-Laplacian inclusions under nonresonance

Antonio Iannizzotto, Eugenio M. Rocha, Sandrina Santos

Abstract:
We study a pseudo-differential inclusion driven by the fractional p-Laplacian operator and involving a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. Using variational methods based on nonsmooth critical point theory (Clarke's subdifferential), we establish existence of at least two constant sign solutions (one positive, the other negative), enjoying Holder regularity.

Submitted February 6, 2018. Published June 15, 2018.
Math Subject Classifications: 35R11, 34A60, 49J92, 58E05.
Key Words: Fractional p-Laplacian; differential inclusion; nonsmooth analysis; critical point theory.

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Antonio Iannizzotto
Department of Mathematics and Computer Science
University of Cagliari
Viale L. Merello 92, 09123 Cagliari, Italy
email: antonio.iannizzotto@unica.it
  EugĂ©nio 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
  Sandrina Santos
CIDMA - Center for Research and Development in Mathematics and Applications
Department of Mathematics, University of Aveiro
3810-193 Aveiro, Portugal
email: sras@ua.pt

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