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

2021/05/07 by Anouar Bahrouni, Bahrouni, Anouar, Hlel Missaoui +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.03368

openalex publication_date 2021/05/07 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

Related

• Compact embedding theorems and a Lions' type Lemma for fractional\n Orlicz-Sobolev spaces
• Existence of least energy nodal solution with two nodal domains for a\n generalized Kirchhoff problem in an Orlicz Sobolev space
• The existence of least energy nodal solutions for some class of Kirchhoff equations and Choquard equations
• Existence, unique continuation and symmetry of least energy nodal\n solutions to sublinear Neumann problems
• Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition