## Abstract and Applied Analysis

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

#### Abstract

We study the existence of entire positive solutions for the semilinear elliptic system with quadratic gradient terms, $\mathrm{\Delta }{u}_{i}+|\nabla {u}_{i}{|}^{2}={p}_{i}(|x|){f}_{i}({u}_{1},{u}_{2},\dots ,{u}_{d})$ for $i=1,2,\dots ,d$ on ${R}^{N},N\ge 3$ and $d\in \{1,2,3,\dots \}$. We establish the conditions on ${p}_{i}$ 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 ${f}_{i}$ is simple and different to the Keller-Osserman condition.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 697565, 15 pages.

Dates
First available in Project Euclid: 5 April 2013

https://projecteuclid.org/euclid.aaa/1365168872

Digital Object Identifier
doi:10.1155/2012/697565

Mathematical Reviews number (MathSciNet)
MR2999920

Zentralblatt MATH identifier
1257.35094

#### Citation

Yang, Yongju; Zhang, Xinguang. Entire Blow-Up Solutions of Semilinear Elliptic Systems with Quadratic Gradient Terms. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 697565, 15 pages. doi:10.1155/2012/697565. https://projecteuclid.org/euclid.aaa/1365168872

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