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

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.