Abstract
In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane-Emden system of differential equations:
-u '' = a(x)u(alpha) v(r) in (0, 1),
-v '' = b(x)u(s) v(beta) in (0, 1),
u'(0) - v'(0) - 0; u(1) - v(1) - 0,
where r, s is an element of R, alpha, beta < 1 such that gamma: = (1 - alpha)(1 - beta) - rs > 0 and the nonnegative functions a, b satisfy some conditions related to the Karamata regular variation theory.