Singular perturbations for third-order nonlinear multi-point boundary value problem

This paper is devoted to study the following third-order multi-point singularly perturbed boundary value problem where a,b,c,d 0,A,B R,a+b>0,c+d>0, αi 0,βi 0, i=1,2,…,n-2, 0<ξ1<ξ2< <ξn-2<1, and 0<η1<η2< <ηn-2<1. The existence, uniqueness and asymptotic estimates of solutions of the boundary value problem are give by using priori estimates, differential inequalities technique and Leray–Schauder degree theory.