Volume 26, Issue 1
Existence of Nontrivial Weak Solutions to Quasi-linear Elliptic Equations with Exponential Growth

J. Part. Diff. Eq., 26 (2013), pp. 25-38.

Published online: 2013-03

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• Abstract

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 $u→+∞$.

• Keywords

Trudinger-Moser inequality exponential growth

35J20, 35J60

chongwang@gwu.edu (Chong Wang)

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@Article{JPDE-26-25, author = {Chong and Wang and chongwang@gwu.edu and 12127 and Department of Mathematics, the George Washington University, Washington DC 20052, USA and Chong Wang}, title = {Existence of Nontrivial Weak Solutions to Quasi-linear Elliptic Equations with Exponential Growth}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {1}, pages = {25--38}, abstract = {

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} }
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 -

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 $u→+∞$.

Chong Wang. (2019). Existence of Nontrivial Weak Solutions to Quasi-linear Elliptic Equations with Exponential Growth. Journal of Partial Differential Equations. 26 (1). 25-38. doi:10.4208/jpde.v26.n1.3
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