Singularly perturbed third-order boundary value problem for nonlinear systems

This paper deals with the existence of solutions to a singularly perturbed boundary value problem for third-order nonlinear differential systems. The authors construct an appropriate generalized lower solution-upper solution pair, a concept that is defined in this paper, and employ the method of descent, Nagumo conditions, algebraic boundary layer functions and Volterra type integral operator to guarantee the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems has nonlinear dependence on all over order derivatives of the unknown.