Entire positive solution to the system of nonlinear elliptic equations

The second-order nonlinear elliptic system ￠ ’ ”u=f1(x)u ±+g1(x)u ￠ ’ 2+h1(x)u 3P(v), ￠ ’ ”v=f2(x)v ±+g2(x)v ￠ ’ 2+h2(x)v 3P(u) with 0< ±, 2, 3<1, is considered in ￠ N. 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) ￠ ￠ loc2, ( ￠ N) — ￠ loc2, ( ￠ N)(0< <1) such that both u and v are bounded below and above by positive constant multiples of |x|2 ￠ ’N for all |x| ￠ ‰ ￥1.