Least-energy nodal solutions of nonlinear equations with fractional Orlicz-Sobolev spaces

TL;DR

This paper establishes the existence of least-energy nodal solutions for nonlinear equations involving a fractional Orlicz Laplacian, using compact embeddings, minimization on Nehari manifolds, and deformation techniques.

Contribution

It introduces a new approach to prove existence results for fractional Orlicz Laplacian equations, including compact embedding theorems and variational methods.

Findings

Proved compact embeddings for weighted fractional Orlicz-Sobolev spaces.

Established existence of least-energy nodal solutions.

Applied minimization on Nehari manifold with deformation lemma.

Abstract

In our work, we prove the existence of least-energy nodal solutions for nonlinear equations in which the new fractional Orlicz Laplacian is present. Precisely, we prove a compact embeddings result for weighted fractional Orlicz-Sobolev spaces. Next, by a minimization argument on Nehari manifold and a quantitative deformation lemma, we show our desired result.