Abstract:
We consider the system of integral equations of the form Ax+Vx=\nobreakψ, where V is the Volterra operator with kernel of convolution type
and A is a constant matrix, detA=\nobreak0. We prove an existence
theorem and establish necessary and sufficient conditions for the kernel of
the operator of the system to be trivial.
Keywords:
Volterra integral equation, convolution-type kernel, left regularizing operator, Fredholm operator, integro-differential operator.
Citation:
V. F. Chistyakov, “On Some Properties of Systems
of Volterra Integral Equations of the Fourth Kind
with Kernel of Convolution Type”, Mat. Zametki, 80:1 (2006), 115–118; Math. Notes, 80:1 (2006), 109–113
\Bibitem{Chi06}
\by V.~F.~Chistyakov
\paper On Some Properties of Systems
of Volterra Integral Equations of the Fourth Kind
with Kernel of Convolution Type
\jour Mat. Zametki
\yr 2006
\vol 80
\issue 1
\pages 115--118
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\transl
\jour Math. Notes
\yr 2006
\vol 80
\issue 1
\pages 109--113
\crossref{https://doi.org/10.1007/s11006-006-0114-7}
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Linking options:
https://www.mathnet.ru/eng/mzm2786
https://doi.org/10.4213/mzm2786
https://www.mathnet.ru/eng/mzm/v80/i1/p115
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