Multiple solutions for a fractional Choquard problem with slightly subcritical exponents on bounded domains

2023/02/06 by Marco Ghimenti, Min Liu, Ghimenti, Marco G. +3 · 1 citation
Computer Science · Mathematics · #35J66 #35Q40 #35R11 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.02698

openalex publication_date 2023/02/06 · openalex created_date 2023/02/09 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of the convolution type nonlinearity tends to the fractional critical one in the sense of Hardy-Littlewood-Sobolev inequality, we obtain the existence of multiple positive solutions via Lusternik-Schnirelmann category and nonlocal global compactness. Moreover, we prove that the topology of the domain furnishes a lower bound for the number of positive solutions.

Cited by

• Nonlocal problems with Hardy-Littlewood-Sobolev critical exponent and Hardy potential

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