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Solution of Volterra operator-integral equations in the nonregular case by the successive approximation method |
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| Authors: | N A Sidorov D N Sidorov A V Krasnik |
| Institution: | 1.Irkutsk State University,Irkutsk,Russia;2.Institute of System Dynamics and Control Theory, Siberian Branch,Russian Academy of Sciences,Irkutsk,Russia;3.Institute of Power Engineering Systems, Siberian Branch,Russian Academy of Sciences,Irkutsk,Russia |
| Abstract: | 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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