On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE
A linear first order ordinary differential equation (ODE) with a positive parameter $\varepsilon$ 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 $\varepsil...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EJAAM
2019-12-01
|
| Series: | E-Journal of Analysis and Applied Mathematics |
| Subjects: | |
| Online Access: | https://ejaam.org/articles/2019/10.2478-ejaam-2019-0006.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823864939055415296 |
|---|---|
| author | Dovlet M. Dovletov |
| author_facet | Dovlet M. Dovletov |
| author_sort | Dovlet M. Dovletov |
| collection | DOAJ |
| description | A linear first order ordinary differential equation (ODE) with a positive parameter $\varepsilon$ 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 $\varepsilon$ 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. |
| format | Article |
| id | doaj-art-d9cecdafcfb54b5eb4b1dce4b1c924e3 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2019-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-d9cecdafcfb54b5eb4b1dce4b1c924e32025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902019-12-01201910.2478/ejaam-2019-0006On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODEDovlet M. Dovletov0Department of Mathematics, Near East University, Nicosia, TRNC, Mersin 10, TurkeyA linear first order ordinary differential equation (ODE) with a positive parameter $\varepsilon$ 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 $\varepsilon$ 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.https://ejaam.org/articles/2019/10.2478-ejaam-2019-0006.pdfordinary differential equationpositive parametersmall parametermultipoint problemnonlocal initial value problemnonlocal initial value conditiona uniform on parameter a priori estimatean asymptotic expansionintegral kind of nonlocal initial value condition |
| spellingShingle | Dovlet M. Dovletov On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE E-Journal of Analysis and Applied Mathematics 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 |
| title | On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE |
| title_full | On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE |
| title_fullStr | On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE |
| title_full_unstemmed | On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE |
| title_short | On a multipoint nonlocal initial value problem for a singularly-perturbed first-order ODE |
| title_sort | on a multipoint nonlocal initial value problem for a singularly perturbed first order ode |
| topic | 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 |
| url | https://ejaam.org/articles/2019/10.2478-ejaam-2019-0006.pdf |
| work_keys_str_mv | AT dovletmdovletov onamultipointnonlocalinitialvalueproblemforasingularlyperturbedfirstorderode |