Positive solutions and eigenvalue intervals for nonlinear systems

This paper deals with the existence of positive solutions for the nonlinear system(q (t)phi (p(t)u(i)(t))) + f (t, u) = 0, 0 t 1, i = 1, 2,.....n.This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u(1),...,u(n)) and f(i), i = 1, 2,..., n are continuous and nonnegative functions, p(t), q (t): [0, 1] - (0, infinity) are continuous functions. Moreover, we characterize the eigenvalue intervals for(q(t)phi (p(t)u(i)(t))) + lambda hi (t)g(i) (u) = 0, 0 t 1, i = 1, 2,..., n.The proof is based on a well-known fixed point theorem in cones.