Electron. J. Diff. Equ., Vol. 2010(2010), No. 16, pp. 1-5.

Existence of entire positive solutions for a class of semilinear elliptic systems

Zhijun Zhang

Abstract:
Under simple conditions on $f_i$ and $g_i$, we show the existence of entire positive radial solutions for the semilinear elliptic system
$$\displaylines{ \Delta u =p(|x|)f_1(v)f_2(u)\cr \Delta v =q(|x|)g_1(v)g_2(u), }$$
where $x\in \mathbb{R}^N$, $N\geq 3$, and p,q are continuous functions.

Submitted October 22, 2009. Published January 27, 2010.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Semilinear elliptic systems; entire solutions; existence.

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Zhijun Zhang
School of Mathematics and Information Science
Yantai University, Yantai, Shandong, 264005, China
email:zhangzj@ytu.edu.cn

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