Electron. J. Diff. Equ., Vol. 2011 (2011), No. 39, pp. 1-9.

Existence of entire solutions for semilinear elliptic systems under the Keller-Osserman condition

Zhijun Zhang, Yongxiu Shi, Yanxing Xue

Abstract:
Under the Keller-Osserman condition on $f+g$, we show the existence and nonexistence of entire solutions for the semilinear elliptic system $\Delta u =p(x)f(v), \quad \Delta v =q(x)g(u),\quad x\in \mathbb{R}^N$, where $p,q:\mathbb{R}^N\to [0,\infty)$ are continuous functions.

Submitted January 22, 2011. Published March 9, 2011.
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
Yongxiu Shi
School of Mathematics and Information Science
Yantai University, Yantai, Shandong, 264005, China
email: syxiu0926@126.com
Yanxing Xue
School of Mathematics and Information Science
Yantai University, Yantai, Shandong, 264005, China
email: xiaoxue19870626@163.com

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