This article is cited in 7 papers

On Some Properties of Systems of Volterra Integral Equations of the Fourth Kind with Kernel of Convolution Type

V. F. Chistyakov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider the system of integral equations of the form $Ax+Vx=\nobreak \psi$, where $V$ is the Volterra operator with kernel of convolution type and $A$ is a constant matrix, $\det A=\nobreak 0$. 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.

UDC: 517.968

Received: 13.11.2003
Revised: 28.11.2005

DOI: 10.4213/mzm2786

 English version: Mathematical Notes, 2006, 80:1, 109–113

Bibliographic databases:

• 
• 
• 
• 
•