On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE

Abstract A linear first order ordinary differential equation (ODE) with a positive parameter ɛ and a multipoint nonlocal initial value condition (NLIVC) is considered. The existence of a classical solution of the multipoint nonlocal initial value problem (NLIVP) is proved. A uniform on ɛ a priori estimate and asymptotic expansion of smooth solution is obtained. The differential problem with integral kind of NLIVC is considered and reduced to appropriate multipoint NLIVP.