Ground state solutions of a Choquard type system with critical exponential growth

Abstract

In this paper, we study the existence of ground state solutions for the following Choquard type system $\{\begin{array}{ll}-\mathrm{\Delta }u+u=(I_{\mu }\ast F_1(u))f_1(u)+\lambda (x)v,& x\in {\mathbb{R}}^2,\\ -\mathrm{\Delta }v+v=(I_{\mu }\ast F_2(v))f_2(v)+\lambda (x)u,& x\in {\mathbb{R}}^2,\end{array}$where $I_{\mu }=\frac{1}{|x{|}^{\mu }}$ and $0<\mu <2$, $f_i$ has exponential critical growth of Trudinger-Moser type, $F_i$ is the primitive function of $f_i$ for i = 1, 2, λ is a continuous and periodic function.

Keywords:

• Choquard type system
• critical exponential growth
• ground state solutions

Maths:

• 35J47
• 35J50

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research bas been supported by Natural Science Foundation of Chongqing, China [grant number cstc2021ycjh-bgzxm0115] and Fundamental Research Funds for the Central Universities [grant number XDJK2020B047].