Positive solutions of the second-order differential systems in reactor dynamics

In this paper, we are concerned with the existence of positive solutions of the second-order cooperative system [GRAPHICS] where lambda > -pi(2) is a constant, mu > 0 is a parameter, g : vertical bar 0, 1 vertical bar -> vertical bar 0, infinity) is continuous and g not equivalent to 0 on any subinterval of [0, 1], f : [0, infinity) -> [0, infinity) is continuous and f (s) > 0 for s > 0. Under some suitable conditions on the nonlinearity f, we show that above system has at least one positive solution for any mu is an element of (0, infinity). The proof of our main results is based upon bifurcation techniques. (C) 2012 Elsevier Inc. All rights reserved.