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arXiv 1208.36042012-08-17math.DSmath.FAmath.OC

具有Piecewise Continuous核的第一类Volterra算子方程的解

Solution to the Volterra Operator Equations of the 1st kind with Piecewise Continuous Kernels

Denis Sidorov, Nikolai Sidorov

备注：: 17 pages

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摘要：

给出了具有分段连续核的第一类Volterra算子方程连续解存在唯一的充分条件。在非唯一解的情况下，构造了参数解族的渐近逼近。利用逐次逼近法给出了求解的改进算法。

英文摘要：

The sufficient conditions for existence and uniqueness of continuous solutions of the Volterra operator equations of the first kind with piecewise continuous kernel are derived. The asymptotic approximation of the parametric family of solutions are constructed in case of non-unique solution. The algorithm for the solution's improvement is proposed using the successive approximations method.

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