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Article type: Research Article
Authors: Guan, Minlan | Lai, Lizhen; * | Liu, Boxue | Qin, Dongdong
Affiliations: School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P. R. China
Correspondence: [*] Corresponding author. E-mail: [email protected].
Abstract: In this paper, we study the following Hamilton–Choquard type elliptic system: −Δu+u=(Iα∗F(v))f(v),x∈R2,−Δv+v=(Iβ∗F(u))f(u),x∈R2, where Iα and Iβ are Riesz potentials, f:R→R possessing critical exponential growth at infinity and F(t)=∫0tf(s)ds. Without the classic Ambrosetti–Rabinowitz condition and strictly monotonic condition on f, we will investigate the existence of ground state solution for the above system. The strongly indefinite characteristic of the system, combined with the convolution terms and critical exponential growth, makes such problem interesting and challenging to study. With the help of a proper auxiliary system, we employ an approximation scheme and the non-Nehari manifold method to control the minimax levels by a fine threshold, and succeed in restoring the compactness for the critical problem. Existence of a ground state solution is finally established by the concentration compactness argument and some detailed estimates.
Keywords: Hamilton–Choquard elliptic system, Critical exponential growth, Ground state solution, Trudinger–Moser inequality
DOI: 10.3233/ASY-241916
Journal: Asymptotic Analysis, vol. 140, no. 3-4, pp. 159-189, 2024
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