Spectral problem for a Fredholm second-order integro-differential equation

1Yuldashev, TK
1Siberian State Aerospace University, Krasnoyarsk, Russia
Dopov. Nac. akad. nauk Ukr. 2018, 12:3-13
https://doi.org/10.15407/dopovidi2018.12.003
Section: Mathematics
Language: Russian
Abstract: 

The questions of existence and construction of solutions of a homogeneous boundary value-problem for a second-order Fredholm integro-differential equation with degenerate kernel and with spectral parameter are considered. The singularities that arise in the construction of solutions and are associated with the definition of arbitrary (unknown) constants are studided. The values of spectral parameters, for which the solvability of the boundary-value problem is proved and the corresponding solutions are constructed, are calculated.

Keywords: degenerate kernel, integro-differential equation, solvability, spectral parameter, spectral problem
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