Nontrivial solutions for nonlinear problems driven by a superposition of fractional p-Laplacians with Neumann boundary conditions

TL;DR

This paper establishes the existence of nontrivial solutions for nonlinear nonlocal problems involving superpositions of fractional p-Laplacians with Neumann boundary conditions, using variational methods.

Contribution

It introduces a general framework for analyzing nonlinear problems with superposed fractional p-Laplacians and applies spectral and variational techniques to prove solution existence.

Findings

Existence of solutions established under broad conditions.

Application of mountain pass and linking methods.

Framework applicable to various specific cases.

Abstract

In this paper, we investigate existence results for nonlinear nonlocal problems governed by an operator obtained as a superposition of fractional $p$-Laplacians, subject to Neumann boundary conditions. A spectral analysis of the main operator leads us to apply different variational tools to establish our results. Specifically, we will use either the mountain pass method or the technique of linking over cones. Due to the generality of the setting, the resulting theory applies to a wide range of specific situations.