Multiple solutions for superlinear fractional $p$-Laplacian equations

TL;DR

This paper establishes the existence of multiple solutions for a class of superlinear fractional p-Laplacian equations using advanced variational methods, even without the Ambrosetti-Rabinowitz condition.

Contribution

It introduces new techniques to find multiple solutions for fractional p-Laplacian problems with superlinear reactions without relying on the Ambrosetti-Rabinowitz condition.

Findings

Proved at least three nontrivial solutions exist.

Applied critical point, truncation, and Morse theory methods.

Extended solution existence results to degenerate or singular fractional p-Laplacian equations.

Abstract

We study a Dirichlet problem driven by the (degenerate or singular) fractional $p$-Laplacian and involving a $(p-1)$-superlinear reaction at infinity, not necessarily satisfying the Ambrosetti-Rabinowitz condition. Using critical point theory, truncation, and Morse theory, we prove the existence of at least three nontrivial solutions to the problem.