Nonlocal elliptic equation with critical exponential growth and resonance in high-order eigenvalues - Li, Shuoshuo; Shen, Zifei; Zhou, Jiazheng (Topological Methods in Nonlinear Analysis, 2021)
In this paper we are interested in the following nonlocal elliptic equation cases -Δ u=λ_ku+[1|x|^μ * G(x,u)]g(x,u) &in Ω, u=0 &on Ω, cases where an open ΩR^2 is bounded with smooth boundary. The nonlinearity g(x,s) has the critical exponential growth in the sense of the Trudinger-Moser inequality and λ_k denotes the kth eigenvalue of (-Δ,H_0^1(Ω)), k≥2. Employing variational methods we prove the existence of a nontrivial solution for this nonlocal elliptic problem.