On critical N‐Kirchhoff type equations involving Trudinger–Moser nonlinearity.

In the present paper, we deal with the existence of nontrivial solutions and Nehari‐type ground state solutions to the Kirchhoff type elliptic equations of the form: −M‖∇u‖NNΔNu=f(x,u),inΩ,u=0,on∂Ω,where Ω⊂ℝN(N≥2) is a smooth bounded domain, M:ℝ+→ℝ+ is a Kirchhoff function, and f(x, s) has critical exponential growth on s which behaviors as eα0s2 with α0 > 0. Based on a deep analysis and some detailed estimate, we can determine a fine upper bound for the minimax level under weaker assumption on lim inft→∞tf(x,t)expα0tN/(N−1). Our results generalize and improve the ones in Chen et al. (2021) (Lemma 3.1) and Figueiredo and Severo (2016) (Theorems 1.3 and 1.4) for N=2 and Goyal et al. (2016) (Theorem 1.3) for N ≥ 2. [ABSTRACT FROM AUTHOR]