Abstract and Applied Analysis
Volume 2012 (2012), Article ID 697565, 15 pages
http://dx.doi.org/10.1155/2012/697565
Research Article

Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms

Yongju Yang1 and Xinguang Zhang2

1School of Mathematics and Statistics, Nanyang Normal University, Henan, Nanyang 473061, China
2School of Mathematical and Informational Sciences, Yantai University, Shandong, Yantai 264005, China

Received 1 September 2012; Accepted 8 November 2012

Academic Editor: Yong Hong Wu

Copyright © 2012 Yongju Yang and Xinguang Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, for on and . We establish the conditions on that ensure the existence of nonnegative radial solutions blowing up at infinity and also the conditions for bounded solutions on the entire space. The condition on is simple and different to the Keller-Osserman condition.