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The existence of multiple solutions for a class of upper critical Choquard equation in a bounded domain

Chen Yongpeng, Yang Zhipeng

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230152

In this article, we consider the following Choquard equation with upper critical exponent: [formula], x ∈ Ω where μ > 0 is a parameter, N > 4, 0 < α < N , […] is the Riesz potential, […] is a bounded domain with smooth boundary, and ƒ and g are continuous functions. For μ small enough, using variational methods, we establish the relationship between the number of solutions and the profile of potential g.