Positive solutions and eigenvalue intervals for nonlinear systems

Abstract

This paper deals with the existence of positive solutions for the nonlinear system $$ (q(t)\phi (p(t)u'_i (t)))' + f^i (t,u) = 0, 0 < t < 1, i = 1,2, \ldots ,n $$ . This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u1, …, un) and fi, i = 1, 2, …, n are continuous and nonnegative functions, p(t), q(t): [0, 1] → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for $$ (q(t)\phi (p(t)u'_i (t)))' + \lambda h_i (t)g^i (u) = 0, 0 < t < 1, i = 1,2, \ldots ,n $$ . The proof is based on a well-known fixed point theorem in cones.