Solution of Volterra operator-integral equations in the nonregular case by the successive approximation method
The branches of solutions of a nonlinear integral equation of Volterra type in a Banach space are constructed by the successive approximation method. We consider the case in which a solution may have an algebraic branching point. We reduce the equation to a system regular in a neighborhood of the br...
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Veröffentlicht in: | Differential equations 2010-06, Vol.46 (6), p.882-891 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | The branches of solutions of a nonlinear integral equation of Volterra type in a Banach space are constructed by the successive approximation method. We consider the case in which a solution may have an algebraic branching point. We reduce the equation to a system regular in a neighborhood of the branching point. Continuous and generalized solutions are considered. General existence theorems are used to study an initial-boundary value problem with degeneration in the leading part. |
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ISSN: | 0012-2661 1608-3083 |
DOI: | 10.1134/S001226611006011X |