The Nehari manifold for fractional p-Laplacian system involving concave-convex nonlinearities and sign-changing weight functions

TL;DR

This paper investigates a fractional p-Laplacian system with nonlinearities and sign-changing weights, demonstrating the existence of multiple solutions using the Nehari manifold approach in bounded domains.

Contribution

It introduces a novel application of the Nehari manifold to establish multiple solutions for a fractional p-Laplacian system with complex nonlinearities and weights.

Findings

Existence of at least two nontrivial solutions for certain parameter ranges.

Application of Nehari manifold method to fractional p-Laplacian systems.

Results extend understanding of nonlinear PDEs with sign-changing weights.

Abstract

In this paper, we consider a fractional p-Laplacian system with both concave-convex nonlinearities and sign-changing weight functions in bounded domains. With the help of the Nehari\ manifold, we prove that the system has at least two nontrivial solutions when the pair of the parameters $(\lambda,\mu)$ belongs to a certain subset of $\mathbb{R}^{n}$