Boundary Value Problems
Volume 2006 (2006), Article ID 32492, 11 pages
doi:10.1155/BVP/2006/32492

Entire positive solution to the system of nonlinear elliptic equations

Lingyun Qiu1,2 and Miaoxin Yao1,2

1Department of Mathematics, Tianjin University, Tianjin 300072, China
2Liu Hui Center for Applied Mathematics, Nankai University and Tianjin University, Tianjin 300072, China

Received 8 November 2005; Revised 12 May 2006; Accepted 15 May 2006

Copyright © 2006 Lingyun Qiu and Miaoxin Yao. 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

The second-order nonlinear elliptic system −Δu=f1(x)uα+g1(x)u−β+h1(x)uγP(v), −Δv=f2(x)vα+g2(x)v−β+h2(x)vγP(u) with 0<α,β,γ<1, is considered in ℝN. Under suitable hypotheses on functions fi, gi, hi(i=1,2), and P, it is shown that this system possesses an entire positive solution (u,v)∈ℂloc2,θ(ℝN)×ℂloc2,θ(ℝN)(0<θ<1) such that both u and v are bounded below and above by positive constant multiples of |x|2−N for all |x|≥1.