Registration Number
0226U004207,
(0123U100249)
, R & D reports
Title
Study of normally solvable boundary value problems in Banax spaces
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Дослідження нормально розв’язних крайових задач у банаxових просторах
Head
Zhuravlov Valerii P., Доктор фізико-математичних наук
Registration Date
14-07-2026
Organization
Polissya National University
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The goal of the study is to obtain using the theory of the generalized inversion of normally solvable operators and the generalized inversion of integral operators:
- solvability criteria and the form of general solutions of integro-differential equations with degenerate and non-degenerate kernels and boundary value problems for them in Banax and Hilbert spaces.
- solvability criteria and the general form of solutions of integro-differential equations with a degenerate and non-degenerate kernel with control in Banach and Hilbert spaces. Get an image of the general view of the control where these junctions exist.
- obtain formulas for the generalized inversion of (2 x 2)-dimensional operator matrices in Banax spaces, solvability conditions and the form of general solutions of operator equations with such matrices.
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The research report is presented on 17 pages and includes 14 references.
The aim of the study is:
The development of a general theory for establishing solvability and constructing general solutions of linear, weakly perturbed, and weakly nonlinear integral and integro-differential Fredholm equations with degenerate and non-degenerate kernels, as well as boundary value problems for such equations in Banach and Hilbert spaces.
Using the general theory of boundary value problems, the study also aims to establish controllability conditions and general control mechanisms for integral and integro-differential Fredholm equations with degenerate and non-degenerate kernels, and for their associated boundary value problems in Banach and Hilbert spaces.
Another objective is to solve related problems of generalized inversion of two-dimensional operator matrices.
The objectives of the research involved:
Establishing criteria for the solvability of linear integral and integro-differential Fredholm equations with degenerate and non-degenerate kernels and the corresponding boundary value problems in Banach and Hilbert spaces; investigating the existence and uniqueness of solutions to weakly perturbed and weakly nonlinear boundary value problems; obtaining controllability conditions for integro-differential Fredholm equations with degenerate kernels; developing a bifurcation theory of solutions to the corresponding problems; and designing methods for the generalized inversion of operator matrices in finite-dimensional and infinite-dimensional spaces.
Product Description
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Maryna V. Rassadkina
Nataliia V. Honhalo
Mykola P. Fomin
Iryna P. Sliusarenko
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2026-07-14
