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Том 226, № 3 (2017)
- Год: 2017
- Статей: 9
- URL: https://journals.rcsi.science/1072-3374/issue/view/14861
Article
A Coupled System of Nonlocal Fractional Differential Equations with Coupled and Uncoupled Slit-Strips-Type Integral Boundary Conditions
Аннотация
The paper deals with with the existence and uniqueness of solutions for a coupled system of fractional differential equations with coupled and uncoupled slit-strips-type integral boundary conditions. The existence and uniqueness of solutions is established by using the Banach contraction principle, while the existence of solutions is obtained by using the Leray–Schauder alternative. The results are explained with the help of examples.
175-196
197-239
Asymptotically Optimal Control in a Linear Control System with Fast and Slow Variables
Аннотация
The problem of optimal control is described by a system of differential equations with fast and slow variables and by a terminal quality criterion. The control used in the problem is linear. We prove that the optimal control in the averaged problem is asymptotically optimal for the initial problem.
240-253
A Noetherian Impulsive Control Problem
Аннотация
We establish conditions under which an unsolvable degenerate impulsive problem can be made solvable by introducing control functions both in the differential system and in the impulsive condition under the assumption that the degenerate differential system without control can be reduced to a central canonical form.
254-259
Frequency Conditions for the Convergence of Control Systems in a Neighborhood of the Program Manifold
Аннотация
We study conditions for the convergence of nonlinear control systems in a neighborhood of the program manifold. Sufficient conditions of convergence are obtained for the basic control system. We establish the frequency conditions guaranteeing the convergence of the program manifold with respect to a vector function ω:We also find a sufficient condition and a necessary and sufficient condition for the convergence with respect to a parameter.
260-269
General Averaging Scheme for Discrete Equations with Variable Delay
Аннотация
We consider a system of discrete equations containing variable delays and apply the averaging method to find the solution of this system. We propose new procedures for taking into account a given variable delay in the solution of the averaged system. It is shown that the solutions of the averaged and original systems are close.
270-284
Bifurcation of Self-Excited Vibrations for Parabolic Systems with Retarded Argument and Weak Diffusion
Аннотация
We prove the existence of periodic solutions of an autonomous parabolic system of differential equations with retarded argument and weak diffusion on a circle. The problems of existence and stability of traveling waves in the equation of spin combustion with delay are investigated.
285-295
Conditions of Solvability of Functional Equations with Differentiable λ-Injective Operator
Аннотация
We establish conditions for the invertibility of differentiable λ-injective maps in arbitrary Banach spaces, as well as the conditions of existence and uniqueness of bounded and almost periodic solutions of nonlinear difference equations.
296-306
307-334