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Том 222, № 3 (2017)
- Год: 2017
- Статей: 13
- URL: https://bakhtiniada.ru/1072-3374/issue/view/14818
Article
205-213
Boundary-Value Problems with Initial Jumps for Singularly Perturbed Integrodifferential Equations
Аннотация
We study a two-point boundary-value problem for singularly perturbed third-order integrodifferential equations with small parameters at two higher derivatives. The asymptotic convergence of the solution of this problem to the solution of a certain degenerate boundary-value problem is established.
214-225
226-236
On the Solutions of Systems of Nonlinear Functional Equations Continuous in t ∈
Аннотация
For a broad class of systems of nonlinear functional equations, we establish conditions for the existence and uniqueness of continuous solutions. A method for the construction of solutions of this kind and investigation of their properties as ε → 0 is proposed.
237-254
General Form of Generalized Invertible Operators in Banach Spaces
Аннотация
We prove theorems on the general form of generalized invertible operators in Banach spaces in the case where the operators are topologically Noetherian or topologically Fredholm. These theorems generalize the well-known Nikol’skii theorem on the general form of Fredholm operators and the Atkinson theorem on the general form of Noetherian operators in function spaces.
255-265
Noetherian Boundary-Value Problems for Integral Equations
Аннотация
We establish necessary and sufficient conditions for solvability and determine the general form of the solutions of a linear integral equation (with square summable kernel) and a boundary-value problem for equations of this kind.
266-275
Conditions for the Existence of Optimal Control for Some Classes of Differential Equations on Time Scales
Аннотация
We consider a class of problems of optimal control on finite and infinite time scales. For these problems, we establish sufficient conditions for the existence of optimal control formulated in terms of the right-hand sides of the system and the function appearing in the quality criterion.
276-295
Energy Redistribution Between the Reservoir and Liquid with Free Surface for Angular Motions of the System
Аннотация
We study the problem of motion of a cylindrical reservoir (on a pendulum suspension) partially filled with an ideal liquid. At the initial time, the deviation of reservoir from the equilibrium position is described by a certain angle. We analyze the redistribution of kinetic energy in the system and explain the decay of the surface wave motion. The accumulated results qualitatively agree with the available experimental data.
296-303
Wong’s Oscillation Theorem for the Second-Order Delay Differential Equations
304-311
Hyperbolic Invariant Tori of a Fast-Slow System with Dynamic Bifurcation of Multifrequency Oscillations
Аннотация
We present additional information on the dynamics of a fast-slow system with dynamic bifurcation of multifrequency oscillations. It is shown that, parallel with an asymptotically stable invariant torus, the system also possesses hyperbolic invariant tori of lower dimensions located within a small neighborhood of its invariant manifold of slow motions.
312-335
Sensitivity of an Induced System on a Segment
Аннотация
We consider dynamical systems (C (I), f) in which the function f maps a segment I into itself and is naturally extended to closed connected subsets of this segment. For the indicated systems, we study their sensitivity to initial conditions. In particular, it is shown that the system (C (I), f) always possesses a Lyapunov-stable point.
336-344
Representation of Solutions of Linear Differential Systems of the Second Order with Constant Delays
Аннотация
We deduce representations for the solutions of initial-value problems for n-dimensional differential equations of the second order with delays:
and
by using special delay matrix functions. Here, A and B are commuting (n × n)-matrices and τ > 0. Moreover, a formula connecting the delay matrix exponential function with delayed matrix sine and delayed matrix cosine is obtained. We also discuss common features of the considered equations.
345-358
359-365