Geodesic
About the solvability of systems of integral equations with different degrees of differences in kernels
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2009), pp. 87-95.

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The work defines the conditions of solvability of one system of integral convolutional equations with different degrees of differences in kernels. Such the system of the integral convolutional equations has not been studied earlier, and it turned out that all the methods used for the investigation of such a system with the help of Riemann boundary problem at the real axis can not be applied there. The investigation of such a type of the system of equations is based on the investigation of the equivalent system of singular integral equations with the Cauchy type kernels at the real axis. It is determined that the system of the equations is not a Noetherian one. Besides, we have shown the number of the linear independent solutions of the homogeneous system of equations and the number of conditions of solvability for the system of heterogeneous equations. The general form of these conditions is also shown and the spaces of solutions of that system of equations are determined. Thus the system of the convolutional equations that hasn't been studied earlier is presented in that work and the theory of its solvability is built here. So some new and interesting theoretical results are got in the paper. 
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V. I. Neaga; A. G. Scherbakova. About the solvability of systems of integral equations with different degrees of differences in kernels. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2009), pp. 87-95. http://geodesic.mathdoc.fr/item/BASM_2009_1_a8/

[1] Gakhov F. D., Boundary problems, Nauka, Moskva, 1977 (in Russian) | MR | Zbl

[2] Gakhov F. D., Cherski Y. I., Convolutional type equations, Nauka, Moskva, 1978 (in Russian) | MR | Zbl

[3] Gohberg I. Ts., Feldman I. A., The equations in convolutions and the projectional methods of their resolving, Nauka, Moskva, 1971 (in Russian) | MR

[4] Litvinchyuk G. S., Boundary problems and singular integral equations with displacement, Nauka, Moskva, 1977 (in Russian)

[5] Muskhelishvili N. I., Singular integral equations, Nauka, Moskva, 1968 (in Russian) | MR | Zbl

[6] Presdorf Z., Some classes of singular integral equations, Mir, Moskva, 1979 (in Russian) | MR

[7] Tikhonenko N. Y., Melnik A. S., “Solvability and properties of solutions of singular integro-differential equations on the real axis”, Different. Equations, 38:9 (2002), 1218–1224 (in Russian) | DOI | MR | Zbl

[8] Tikhonenko N. Y., Svyagina N. N., “On the compactness of a commutator on the real axis”, Izv. Vuzov. Math., 1996, no. 9, 83–87 (in Russian) | MR | Zbl

[9] Tikhonenko N. Y., Scherbakova A. G., “Solvability and properties of the solutions of integral equations of convolution type with power-difference kernels”, Different. Equations, 40:10 (2004), 1219–1224 (in Russian) | MR | Zbl

[10] Scherbakova A. G., Boundary problems, 11 (2004), 204–211 (in Russian)