Existence of the solution of a boundary value problem for a system of first order ordinary differential equations with multipoint-functional boundary conditions
Uložené v:
| Názov: | Existence of the solution of a boundary value problem for a system of first order ordinary differential equations with multipoint-functional boundary conditions |
|---|---|
| Autori: | Korchak, B. E., Ponomarev, V. D. |
| Informácie o vydavateľovi: | Zinatne, Riga |
| Predmety: | Nonlinear boundary value problems for ordinary differential equations, Nonlocal and multipoint boundary value problems for ordinary differential equations |
| Popis: | Let \(I=[a,b]\), \(f_ i:I\times R^ n\to R\) be of Caratheodory type, and \(\phi_ i:R^ 2\to R\) continuous for \(1\leq i\leq n\). Consider the BVP (*) \(x_ i=f_ i\) \((t,x_ 1,...,x_ n)\), \(\phi_ i(x_ i(a_ i)\), \(x_ i(b_ i))=\phi_ i(x_ 1,...,x_ n)\), where \(\phi_ i's\) are continuous functionals on the space of absolutely continuous functions and \(a\leq a_ i\leq b_ i\leq b\). The authors give some (complex) conditions for the solvability in a generalized sense of BVP(*) both in the regular as well as the singular cases. The results extend some of the earlier ones by \textit{I. T. Kiguradze} and \textit{P. Puža} [Differ. Uravn. 12, 2139-2148 (1976; Zbl 0355.34009)] and \textit{B. Pužha} [Arch. Math. 13, 207-226 (1977; Zbl 0397.34028)]. |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| Prístupová URL adresa: | https://zbmath.org/3877563 |
| Prístupové číslo: | edsair.c2b0b933574d..af31473e23746fa43048a24b7e1ea4ba |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | Let \(I=[a,b]\), \(f_ i:I\times R^ n\to R\) be of Caratheodory type, and \(\phi_ i:R^ 2\to R\) continuous for \(1\leq i\leq n\). Consider the BVP (*) \(x_ i=f_ i\) \((t,x_ 1,...,x_ n)\), \(\phi_ i(x_ i(a_ i)\), \(x_ i(b_ i))=\phi_ i(x_ 1,...,x_ n)\), where \(\phi_ i's\) are continuous functionals on the space of absolutely continuous functions and \(a\leq a_ i\leq b_ i\leq b\). The authors give some (complex) conditions for the solvability in a generalized sense of BVP(*) both in the regular as well as the singular cases. The results extend some of the earlier ones by \textit{I. T. Kiguradze} and \textit{P. Puža} [Differ. Uravn. 12, 2139-2148 (1976; Zbl 0355.34009)] and \textit{B. Pužha} [Arch. Math. 13, 207-226 (1977; Zbl 0397.34028)]. |
|---|