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Vol 220, No 4 (2017)
- Year: 2017
- Articles: 9
- URL: https://journal-vniispk.ru/1072-3374/issue/view/14801
Article
Dichotomy on Semiaxes and the Solutions of Linear Systems with Delay Bounded on the Entire Axis
Abstract
By using the theory of generalized inverse operators, we obtain a criterion for the existence and the general form of solutions of linear inhomogeneous functional-differential systems with delay bounded on the entire real axis in the case where the corresponding homogeneous system with delay is exponentially dichotomous on the semiaxes.
377-393
Weakly Nonlinear Impulsive Problems for Degenerate Differential Systems
Abstract
We study the structure of solutions of degenerate weakly nonlinear differential-algebraic systems with impulsive actions at fixed times. The necessary and sufficient conditions for the existence of solutions of these problems are established and the relationship between the indicated conditions is obtained. An iterative procedure is proposed for finding the solutions of the problem.
394-401
Bargmann-Type Finite-Dimensional Reductions of the Lax-Integrable Supersymmetric Boussinesq Hierarchy and Their Integrability
Abstract
For the supersymmetric Boussinesq hierarchy connected with the Lax-type flows on the space dual to the Lie algebra of superintegrodifferential operators of one anticommuting variable for some nonself-adjoint superdifferential operator, we develop the method of Bargmann-type finite-dimensional reductions. We establish the existence of an exact even supersymplectic structure on the corresponding invariant finite-dimensional supersubspace of the supersymmetric Boussinesq hierarchy, as well as the Lax–Liouville integrability of commuting vector fields, generated by the hierarchy and reduced to this supersubspace.
402-424
425-439
On the Unique Solvability of the Boundary-Value Problems for Fredholm Integrodifferential Equations with Degenerate Kernel
Abstract
We study a linear boundary-value problem for systems of Fredholm integrodifferential equations with degenerate kernels and present the definition of ν-regular partition of the interval. The coefficient necessary and sufficient conditions for the unique solvability of the considered problem are established.
440-460
On Higher-Order Generalized Emden-Fowler Differential Equations with Delay Argument
Abstract
We consider a differential equation
It is assumed that n ≥ 3, p ∈ Lloc(R+;R−), μ ∈ C(R+;(0,+∞)), τ ∈ C(R+;R+), τ(t) ≤ t for t ∈ R+ and limt→+∞τ(t) = +∞. In the case μ(t) ≡ const > 0, the oscillatory properties of equation (*) are extensively studied, whereas for μ(t) ≢ const, to the best of authors’ knowledge, problems of this kind were not investigated at all. We also establish new sufficient conditions for the equation (*) to have Property B.
461-482
On the Robust Stabilization of One Class of Nonlinear Discrete Systems
Abstract
We study the problem of robust linear stabilization of a family of nonlinear discrete control systems with uncertainties and nonlinearly dependent control. We establish sufficient conditions for the robust stabilization and synthesize linear regulators of state engaged in the robust stabilization. The obtained necessary conditions for the robust stabilization are close to sufficient.
483-497
Cross-Like Surface Waves Between Finite Cylindrical Shells
Abstract
We construct a new mathematical model of the interaction of two resonant surface waves in a volume between two cylindrical shells of finite length. For the first time, we establish the existence of chaotic attractors for a system satisfying the resonance conditions for cross-like and forced waves. We also study the regular modes in the system and describe their phase portraits and frequency spectra.
498-513
On the Construction of Coordinate Functions for the Ritz Method in the Numerical Analysis of Nonaxially Symmetric Eigenoscillations of a Dome-Shaped Shell of Revolution
Abstract
We propose systems of coordinate functions that can be used in the Ritz method aimed at finding the natural modes and eigenfrequencies of nonaxially symmetric oscillations of thin-walled dome-shaped shells of revolution. The basis functions are constructed with regard for the specific features of the spectral problem, which guarantees the uniform convergence of the process of calculations. As an example, we find the dynamic characteristics for a shell in the form of a spherical dome.
514-532