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DOI: 10.23671/VNC.2016.2.5921

Inverse Problem for a Third Order Fredholm Integro-Differential Equation with Degenerate Kernel

Yuldashev T. K.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 2.
Abstract:
It is considered the questions of one value solvability of the inverse problem for a third order nonlinear partial Fredholm type integro-differential equation with degenerate kernel. The method of degenerate kernel for second kind Fredholm integral equations is modified for the case of third order partial Fredholm type integro-differential equation. The Fredholm type integro-differential equation is reduced to a system of algebraic equations. By the aid of additional condition it is obtained a second kind nonlinear Volterra type integral equation with respect to main unknown function and a first kind linear Volterra type integral equation with respect to restore function. It is used the method of compressing maps, which gave us the real method of finding the solutions - the method of successive approximations. Further is defined the restore function.
Keywords: inverse problem, integro-differential equation, Fredholm type equation, degenerate kernel, system of algebraic equations, one valued solvability.
Language: Russian Download the full text  
For citation: Yuldashev T. K. Inverse problem for a third order fredholm integro-differential equation with degenerate kernel // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol.19, no. 2, pp. 76-85. DOI 10.23671/VNC.2016.2.5921
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