# Chuiko S. M.

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

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

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.

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

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.

### Weakly nonlinear boundary-value problem in a special critical case

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.

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

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.

### Bifurcation of solutions of a linear Fredholm boundary-value problem

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.

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

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

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.

### Periodic solutions of autonomous systems with pulse influence in critical cases

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.