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

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.

The article has been revised based on a referee's suggestions. We improve the exposition, add results and details. 19 pages

References in corpus (3)

• The second eigenvalue of the fractional $p-$Laplacian
• Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations
• Global bifurcation for fractional $p$-Laplacian and application