Multiplicity results for non-local elliptic problems with jumping nonlinearity

TL;DR

This paper investigates fractional p-Laplacian boundary value problems with jumping nonlinearities, establishing the existence of multiple and sign-changing solutions through variational methods and pseudo-gradient vector fields.

Contribution

It introduces new techniques to prove multiple solutions for non-local elliptic problems with jumping nonlinearities, expanding the understanding of solution multiplicity in such contexts.

Findings

Existence of multiple solutions established.

Sign-changing solutions are obtained.

Use of pseudo-gradient vector fields is demonstrated.

Abstract

The present paper studies the fractional $p$-Laplacian boundary value problems with jumping nonlinearities at zero or infinity and obtain the existence of multiple solutions and sign-changing solutions by constructing the suitable pseudo-gradient vector field of the corresponding energy functional.