Infinite Systems of Hyperbolic Functional Differential Equations
We consider initial-value problems for infinite systems of first-order partial functional differential equations. The unknown function is the functional argument in equations and the partial derivations appear in the classical sense. A theorem on the existence of a solution and its continuous depend...
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| Date: | 2003 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2003
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/164380 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Infinite Systems of Hyperbolic Functional Differential Equations / Z. Kamont // Український математичний журнал. — 2003. — Т. 55, № 12. — С. 1678–1696. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider initial-value problems for infinite systems of first-order partial functional differential equations. The unknown function is the functional argument in equations and the partial derivations appear in the classical sense. A theorem on the existence of a solution and its continuous dependence upon initial data is proved. The Cauchy problem is transformed into a system of functional integral equations. The existence of a solution of this system is proved by using integral inequalities and the iterative method. Infinite differential systems with deviated argument and differential integral systems can be derived from the general model by specializing given operators. |
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