In this paper, we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations $$-Δ_nu+V(x)|u|^{n-2}u=\frac{f(x,u)}{|x|^β}, x ∈ R^n(n ≥ 2),$$ where $-Δ_nu=-div(|∇u|^{n-2}∇u), 0 ≤β < n, V:R^n→R$ is a continuous function, f (x,u) is continuous in $R^n×R$ and behaves like $e^{αu^{\frac{n}{n-1}}}$ as $u→+∞$.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/5151.html} }