Existence and multiplicity of positive solutions for the fractional Laplacian under subcritical or critical growth

2020/04/06 by Silvia Frassu, Frassu, Silvia, Antonio Iannizzotto +1
Computer Science · Mathematics · #35A15 #35R11 #35S15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #msc:35A15 #msc:35R11 #msc:35S15

paper · pdf · doi:10.48550/arxiv.2004.02776

15 pages

arxiv created 2020/04/06 · openalex publication_date 2020/04/06 · arxiv updated 2020/04/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study a Dirichlet type problem for an equation involving the fractional Laplacian and a reaction term subject to either subcritical or critical growth conditions, depending on a positive parameter. Applying a critical point result of Bonanno, we prove existence of one or two positive solutions as soon as the parameter lies under a (explicitly determined) threshold. As an application, we find two positive solutions for a fractional Brezis-Nirenberg problem.

Related

• Existence, Nonexistence, and Symmetry of Positive Solutions for Fractional Laplacian Problems
• Multiplicity results for fractional Laplace problems with critical growth
• Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity
• Bifurcation and multiplicity results for critical fractional p-Laplacian problems
• Bifurcation-type results for the fractional p-Laplacian with parametric nonlinear reaction