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

TL;DR

This paper investigates a fractional Choquard problem with slightly subcritical exponents on bounded domains, establishing the existence of multiple positive solutions influenced by domain topology.

Contribution

It introduces new existence results for multiple solutions using Lusternik-Schnirelmann theory and analyzes the impact of domain topology on solution count.

Findings

Existence of multiple positive solutions near critical exponent

Use of Lusternik-Schnirelmann category to estimate solutions

Topology of the domain provides a lower bound for solutions

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.