2019
Том 71
№ 6

All Issues

Chuiko S. M.

Articles: 7
Article (Ukrainian)

Least-squares method in the theory of matrix differential-algebraic boundary-value problems

Chuiko S. M., Dzyuba M. V., Nesmelova O. V.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 280-292

We use the scheme of the classical least-squares method for the construction of approximate pseudosolutions of a linear matrix boundary-value problem for a system of differential-algebraic equations.

Article (Ukrainian)

Least-squares method in the theory of ill-posed linear boundary-value problems with pulse action

Chuiko S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 690–697

We use the scheme of the classic least-squares method for the construction of an approximate pseudosolution of a linear ill-posed boundary-value problem with pulse action for a system of ordinary differential equations in the critical case. The pseudosolution obtained is represented in the form of partial sums of a generalized Fourier series.

Article (Russian)

Weakly nonlinear boundary-value problem in a special critical case

Chuiko S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 4. - pp. 548-562

We investigate the problem of the determination of conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. We consider the special critical case where the equation for finding the generating solution of a weakly nonlinear Noetherian boundary-value problem turns into an identity. We improve the classification of critical cases and construct an iterative algorithm for finding solutions of weakly nonlinear Noetherian boundary-value problems in the special critical case.

Article (Russian)

Method of accelerated convergence for the construction of solutions of a Noetherian boundary-value problem

Boichuk О. A., Chuiko S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1587–1601

We study the problem of finding conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. A new iterative procedure with accelerated convergence is proposed for the construction of solutions of a weakly nonlinear Noetherian boundary-value problem for a system of ordinary differential equations in the critical case.

Brief Communications (Russian)

Bifurcation of solutions of a linear Fredholm boundary-value problem

Chuiko S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 8. - pp. 1148–1152

We establish constructive conditions for the appearance of solutions of a linear Fredholm boundary-value problem for a system of ordinary differential equations in the critical case and propose an iterative procedure for finding these solutions. The range of values of a small parameter for which the indicated iterative procedure is convergent is estimated.

Article (Russian)

Generalized Green operator of a boundary-value problem with degenerate pulse influence

Boichuk О. A., Chuiko E. V., Chuiko S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 588-594

We find necessary and sufficient conditions for solvability of nonhomogeneous linear boundary-value problems for systems of ordinary differential equations with impulsive force in a general case where the number of boundary-value conditions in not equal to the order of the differential systems (Noetherian problems). We construct a generalized Greens's operator for boundary-value problems, not every solution of which can be extended from the left end point to the right end point of the interval where the solution is defined.

Article (Russian)

Periodic solutions of autonomous systems with pulse influence in critical cases

Boichuk О. A., Chuiko S. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1478–1484

We obtain existence conditions and iterative schemes for constructing periodic solution of weakly nonlinear autonomous systems with pulse influence in critical cases.