Asymptotically linear magnetic fractional problems

2023/12/07 by Rossella Bartolo, Pietro d’Avenia, Bartolo, Rossella +3
Computer Science · Mathematics · #35A15 #35S15 #49J35 #58E05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2312.04473

openalex publication_date 2023/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is investigating the existence and multiplicity of weak solutions to non--local equations involving the \em magnetic fractional Laplacian, when the nonlinearity is subcritical and asymptotically linear at infinity. We prove existence and multiplicity results by using variational tools, extending to the magnetic local and non--local setting some known results for the classical and the fractional Laplace operators.

Related

• Nonlinear fractional magnetic Schrödinger equation: existence and multiplicity
• Multiplicity results for fractional magnetic problems involving\n exponential growth
• Magnetic Fractional order Orlicz-Sobolev spaces
• On a fractional magnetic pseudorelativistic operator: properties and applications
• Existence and concentration of nontrivial solutions for a fractional magnetic Schrödinger-Poisson type equation