On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE
Authors: Dovlet M. Dovletov
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2019 · Pages: 84 - 103
Published Online: 16 Dec 2019
Abstract: A linear first order ordinary differential equation (ODE) with a positive parameter εand 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 εa 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.
Keywords: Ordinary differential equation, positive parameter, small parameter, multipoint problem, nonlocal initial value problem, nonlocal initial value condition, a uniform on parameter a priori estimate, an asymptotic expansion, integral kind of nonlocal initial value condition