Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 39, pp. 1-9.
Title: Existence of entire solutions for semilinear
elliptic systems under the Keller-Osserman condition
Authors: Zhijun Zhang (Yantai Univ., Shandong, China)
Yongxiu Shi (Yantai Univ., Shandong, China)
Yanxing Xue (Yantai Univ., Shandong, China)
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 09, 2011.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Semilinear elliptic systems; entire solutions; existence.