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
Hauptverfasser: Sidorov, N. A., Sidorov, D. N., Krasnik, A. V.
Format: Artikel
Sprache:eng
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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.
ISSN:0012-2661
1608-3083
DOI:10.1134/S001226611006011X