2019
Том 71
№ 11

All Issues

Rutkas A. G.

Articles: 5
Article (Russian)

Problem of impulsive regulator for one dynamical system of the Sobolev type

Rutkas A. G., Samoilenko A. M., Vlasenko L. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1027–1034

We establish conditions for the existence of an optimal impulsive control for an implicit operator differential equation with quadratic cost functional. The results obtained are applied to the filtration problem.

Article (Russian)

Solvability of semilinear differential equations with singularity

Rutkas A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 225–239

Local theorems on the existence of solutions of the Cauchy problem for the singular equations of the form $$ \frac{d}{dt}(Au(t)) + Bu(t) = f(t, u)$$ in Banach spaces are proved. The conditions for the solvability depend on a type of the singularity of the sheaf $\lambda A + B$ of closed linear operators $A, B$. Examples and applications to finite-dimensional differential algebraic equations, infinite systems of differential equations, and partial differential equations of non-Kovalevskaya type are presented.

Article (Russian)

Criteria for the Well-Posedness of the Cauchy Problem for Differential Operator Equations of Arbitrary Order

Piven’ A. L., Rutkas A. G., Vlasenko L. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 11. - pp. 1484-1500

In Banach spaces, we investigate the differential equation \(\mathop \sum \nolimits_{j = 0}^n \;A_j u^{(j)} (t) = 0\) with closed linear operators A j (generally speaking, the operator coefficient A n of the higher derivative is degenerate). We obtain well-posedness conditions that characterize the continuous dependence of solutions and their derivatives on initial data. Abstract results are applied to partial differential equations.

Article (Ukrainian)

Perturbations of skew-Hermitian bundles and the degenerate cauchy problem

Rutkas A. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1989. - 41, № 8. - pp. 1082–1088

Article (Ukrainian)

Pairs on non self-adjoint operators and operator hypernodes

Rutkas A. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1970. - 22, № 1. - pp. 37–52