Nonnegative solutions to nonlocal boundary value problems for systems of second-order differential equations dependent on the first-order derivatives

In this paper, we consider nonlocal boundary value problems for systems of second-order differential equations with dependence on the first-order derivatives and deviating arguments. By using a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three nonnegative solutions to such problems. We investigate our problem both for delayed and advanced arguments alpha(i), delta(i) and also for the case when alpha(i)(t) = delta(i)(t) = t, t is an element of [0, 1]. In all cases, arguments beta(i), zeta(i) can change the character on [0, 1], so, in some subinterval I of [0, 1], they can be delayed in I and advanced in [0, 1]\I. Some remarks concern also the case when differential equations do not depend on the first-order derivatives. Examples illustrate some results. (C) 2013 Elsevier Ltd. All rights reserved.