Geodesic
On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 773-789

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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.
Keywords: Volterra operator equation, Banach space, asymptotic approximation, successive approximation method, Fredholm point, Fredholm operator
Mots-clés : Jordan set. 
@article{MZM_2014_96_5_a12,
     author = {N. A. Sidorov and D. N. Sidorov},
     title = {On the {Solvability} of a {Class} of {Volterra} {Operator} {Equations} of the {First} {Kind} with {Piecewise} {Continuous} {Kernels}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {773--789},
     publisher = {mathdoc},
     volume = {96},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a12/}
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N. A. Sidorov; D. N. Sidorov. On the Solvability of a Class of Volterra Operator Equations of the First Kind with Piecewise Continuous Kernels. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 773-789. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a12/