Two solutions for fractional p-Laplacian inclusions under nonresonance

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.

Keywords

• Fractional p-Laplacian
• differential inclusion
• nonsmooth analysis
• critical point theory