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In this paper, we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations -Δ_nu+V(x)|u|^n-2u=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^nn-1 as u→+∞. , number=1, journal=Journal of Partial Differential Equations, year=2018, month=Aug., pages=25–38