A Kirchhoff type elliptic systems with exponential growth nonlinearities - Tian, Xingliang (Topological Methods in Nonlinear Analysis, 2022)
In this paper we are interested in the existence of solutions for the following Kirchhoff type elliptic systems equation* cases -M(^m_j=1\|u_j\|^2)Δ u_i=f_i(x,u_1,…,u_m) &in Ω, %[2mm] u_1=…=u_m=0 &on Ω, cases equation* where Ω is a bounded domain in R^2, M is a Kirchhoff type function, \|u_i\|^2:=_Ω| abla u_i|^2dx, f_i behaves like (β s^2) when |s|→ ∞ for some β> 0, i=1,…,m. By variational methods with the Trudinger-Moser inequality, we obtain the existence of solutions for the above systems.