Existence of positive radial solutions for some nonvariational superlinear elliptic systems

The system under consideration is -Delta u + cu = g(u, v) + u(p), u = u(x), x is an element of B subset of R(N), u vertical bar(partial derivative B) = 0, -Delta v + dv = h(u, v)+ v(q), v = v(x), v vertical bar(partial derivative B) = 0, where c, d >= 0 are constants, B is a ball and 1 < p, q < p* with p* = (N + 2)/(N - 2) if N >= 3 and p* = + infinity if N = 1, 2. Among others, it is assumed that g(0, v) = h(u, 0) = g(u) '(0, v) = h(v)'(u, 0) = 0 and that g and h are nondecreasing functions in each of their arguments obeying certain growth conditions at infinity. We prove the existence of a radial solution ( u, v) satisfying u, v > 0 in B. (C) 2009 Elsevier Inc. All rights reserved.