Two solutions for fractional p-Laplacian inclusions under nonresonance

Antonio Iannizzotto

;Eugénio M. Rocha;Sandrina Santos

2018-01-01

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Abstract

We study a pseudo-differential inclusion driven by the fractional p-Laplacian operator and involving a nonsmooth potential, which satisfies non-resonance conditions both at the origin and at infinity. Using variational meth- ods 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 Hölder regularity.