Positive solutions for second order differential systems with nonlocal conditions

Abstract

A class of second order differential systems with nonlocal conditions is considered under some conditions concerning the first eigenvalue of the relevant linear problem. By constructing a cone K1 × K2 which is the Cartesian product of two cones and computing the fixed point index in K1 × K2, the existence of positive solutions for the systems is established. An example is provided to illustrate the main results.