Multiple solutions for the fractional p-Laplacian with jumping reactions

TL;DR

This paper investigates a nonlinear elliptic equation involving the fractional p-Laplacian with jumping reactions, establishing the existence of multiple solutions using degree theory and spectral analysis under asymmetric conditions.

Contribution

It introduces new existence results for multiple solutions of fractional p-Laplacian problems with jumping reactions under different asymmetry hypotheses.

Findings

Proved existence of at least two nontrivial solutions.

Applied degree theory for monotone operators.

Utilized nonlinear fractional spectral theory.

Abstract

We study a nonlinear elliptic equation driven by the degenerate fractional p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e., (p-1)-linear both at infinity and at zero but with different slopes crossing the principal eigenvalue. Under two different sets of hypotheses, entailing different types of asymmetry, we prove the existence of at least two nontrivial solutions. Our method is based on degree theory for monotone operators and nonlinear fractional spectral theory.