TY - JOUR
T1 - Existence of Nontrivial Weak Solutions to Quasi-linear Elliptic Equations with Exponential Growth
AU - Wang , Chong
JO - Journal of Partial Differential Equations
VL - 1
SP - 25
EP - 38
PY - 2013
DA - 2013/03
SN - 26
DO - http://doi.org/10.4208/jpde.v26.n1.3
UR - https://global-sci.org/intro/article_detail/jpde/5151.html
KW - Trudinger-Moser inequality
KW - exponential growth
AB - <p>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 $-Δ_nu=-div(|∇u|^{n-2}∇u), 0 ≤β &lt; n, V:R^n→R$ is a continuous function, f (x,u) is continuous in $R^n×R$ and behaves like $e^{αu^{\frac{n}{n-1}}}$ as $u→+∞$.</p>