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. 
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/
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