Electron. J. Diff. Eqns., Vol. 2007(2007), No. 53, pp. 1-10.

A remark on ground state solutions for Lane-Emden-Fowler equations with a convection term

Hongtao Xue, Zhijun Zhang

Abstract:
Via a sub-supersolution method and a perturbation argument, we study the Lane-Emden-Fowler equation
$$ -\Delta u =p(x)[g(u)+f(u)+|\nabla u|^q] $$
in $\mathbb{R} ^N$ ($N\geq3$), where 0 less than q less than 1, $p$ is a positive weight such that $\int_0^\infty r\varphi(r)dr$ less than $\infty$, where $\varphi(r)=\max_{|x|=r}p(x)$, $r\geq 0$. Under the hypotheses that both $g$ and $f$ are sublinear, which include no monotonicity on the functions $g(u)$, $f(u)$, $g(u)/u$ and $f(u)/u$, we show the existence of ground state solutions.

Submitted January 6, 2007. Published April 10, 2007.
Math Subject Classifications: 35J60, 35B25, 35B50, 35R05.
Key Words: Ground state solution; Lane-Emden-Fowler equation; convection term; maximum principle; existence; sub-solution; super-solution.

Show me the PDF file (242K), TEX file, and other files for this article.

Hongtao Xue
School of Mathematics and Informational Science
Yantai University, Yantai, Shandong, 264005, China
email: ytxiaoxue@yahoo.com.cn
Zhijun Zhang
Department of Mathematics and Informational Science
Yantai University, Yantai, Shandong, 264005, China
email: zhangzj@ytu.edu.cn

Return to the EJDE web page