Non-resonant Fredholm alternative and anti-maximum principle for the fractional $p-$Laplacian

TL;DR

This paper extends classical results to nonlinear fractional p-Laplacian problems, establishing existence in a non-resonant range and proving an anti-maximum principle for these operators.

Contribution

It introduces the first extension of the Fredholm alternative and anti-maximum principle to nonlinear fractional p-Laplacian equations.

Findings

Existence of solutions in a non-resonant eigenvalue range.

Proof of the anti-maximum principle for the fractional p-Laplacian.

Extension of classical linear results to nonlinear fractional operators.

Abstract

In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional $p-$Laplacian. The first result is a existence in a non-resonant range more specific between the first and second eigenvalue of the fractional $p-$Laplacian. The second result is the anti-maximum principle for the fractional $p-$Laplacian.