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Vol 228, No 3 (2018)
- Year: 2018
- Articles: 10
- URL: https://journal-vniispk.ru/1072-3374/issue/view/14878
Article
181-206
Asymptotics of Slowly Varying Solutions of Ordinary Binomial Differential Equations of the Second Order with Rapidly Varying Nonlinearity
Abstract
We establish the conditions for the existence of one class of solutions of a nonautonomous binomial differential equation of the second order with rapidly varying nonlinearity and the asymptotic representations for these solutions and their first derivatives as t ↑ ω (ω ≤ +∞).
207-225
226-244
Existence of an Optimal Control for Systems of Differential Equations with Pulse Action at Nonfixed Times
Abstract
For systems of differential equations with pulse action at nonfixed times, we establish the conditions for the existence of optimal control. These conditions depend on the right-hand sides of the system and the quality criterion.
245-262
Bounded Solutions of Hyperbolic Boundary-Value Problems
Abstract
We investigate linear boundary-value problems for the first-order one-dimensional hyperbolic systems in a strip and establish conditions for the existence and uniqueness of bounded continuous solutions. For this purpose, we suppose that the nondiagonal part of the zero-order coefficients vanish at infinity. Moreover, we establish a dissipativity condition in terms of the boundary data and determine the diagonal part of the zero-order coefficients.
263-275
Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices
Abstract
In recent results on representation of the solutions of systems of delayed differential equations, the condition that the linear parts are given by pairwise permutable matrices was assumed. We show how this strong condition can be avoided and derive a representation of solutions of systems of differential equations with nonconstant coefficients and variable delays. The results are applied to a system with two constant delays. In addition, the nonexistence of blow-up solutions is proved for nonlinear systems.
276-289
Asymptotically Almost Periodic Solutions of Equations with Delays and Nonfixed Times of Pulse Action
Abstract
By using the properties of asymptotically almost periodic solutions, we prove the theorems on existence of an asymptotically stable piecewise continuous solution of a system of differential equations with delays and nonfixed times of pulse action.
290-305
Approximate Synthesis of Distributed Optimal Control for Hyperbolic Equations with Rapidly Oscillating Coefficients
Abstract
We study the problem of finding approximations to the optimal control with respect to a quadratic-type quality criterion in the form of feedback (synthesis) for a linear-quadratic problem in the from of a hyperbolic equation with rapidly oscillating coefficients and distributed control on the right-hand side. On the basis of the exact formula of synthesis, its approximate version (based on the replacement of the rapidly oscillating variables by averaged quantities) is substantiated.
306-313
On the Stability of Toroidal Manifold for One Class of Dynamical Systems
Abstract
We study the problem of stability of an invariant toroidal manifold for one class of linear extensions of a dynamical system on a torus. The obtained result is used to investigate the problem of existence of invariant manifold for a nonlinear system of differential equations.
314-322
323-334