Singular perturbations of third-order nonlinear differential equations with full nonlinear boundary conditions

In this paper, we discuss singular perturbations of third-order nonlinear ordinary differential equations with full nonlinear boundary conditions. The emphasis here is that the nonlinear term depends on the first, second order derivatives and the boundary conditions are full nonlinear that is where the main novelty of this work lies. By applying the upper and lower solutions method, as well as analysis technique, the existence, uniqueness results for the singularly perturbed boundary value problem are established and asymptotic estimates of solutions is also obtained. (C) 2013 Elsevier Inc. All rights reserved.