Solvability and the determination of the coefficient in a boundary-value problem for a Fredholm-type integro-differential equation with degenerate kernel

1Yuldashev, TK
1Siberian State Aerospace University, Krasnoyarsk, Russia
Dopov. Nac. akad. nauk Ukr. 2017, 5:8-16
Section: Mathematics
Language: Russian

The questions of solvability and determination of the coefficients of a nonlocal boundary-value problem for a second-order Fredholm integro-differential equation with degenerate kernel and reflecting deviation are conside red. The system of algebraic equations is obtained. Some features arising in the determination of the arbitrary (unknown) constants are removed. The criterion of one-value solvability of the considered problem is establi shed. Under this criterion, the one-valued solvability of the problem is proved, and the appropriate therem is proved.

Keywords: degenerate kernel, integral condition, integro-differential equation, inverse boundary-value problem, one-valued solvability
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