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arXiv · 2302.02698

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

Marco G. Ghimenti·Min Liu·Zhongwei Tang
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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.

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Marco G. Ghimenti, Min Liu, Zhongwei Tang. 2023-02-06. Multiple solutions for a fractional Choquard problem with slightly subcritical exponents on bounded domains. https://arxiv.org/abs/2302.02698

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