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On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels

We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind with piecewise determined kernels. For the case in which the solution is not unique, we prove existence theorems for the parametric families of solutions and present their asymptotics in the form of logarithmic polynomials. We obtain sufficient conditions for the existence and uniqueness of continuous solutions of Volterra operator equations of the first kind...

Теги: Volterra operator equation , Banach space , asymptotic approximation , successive
Раздел: ESI SB RAS

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