Geodesic
Solution to the Volterra equations of the 1st kind with discontinuous kernels in the class of generalized functions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 1, pp. 80-95

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Sufficient conditions for existence and uniqueness of solutions of the equations of Volterra equation of the 1st kind with a piecewise continuous kernels in the class of generalized functions with point support are derived. An asymptotic approximation of a parametric family of generalized solutions is constructed. A method of the regular part of the solution’s improvement employs the method of successive approximations.
Keywords: Volterra integral equations; discontinuous kernel; generalized solution; successive approximations. 
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     author = {D. N. Sidorov},
     title = {Solution to the {Volterra} equations of the 1st kind with discontinuous kernels in the class of generalized functions},
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D. N. Sidorov. Solution to the Volterra equations of the 1st kind with discontinuous kernels in the class of generalized functions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 1, pp. 80-95. http://geodesic.mathdoc.fr/item/IIGUM_2012_5_1_a7/