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Vol 212, No 4 (2016)
- Year: 2016
- Articles: 9
- URL: https://journals.rcsi.science/1072-3374/issue/view/14709
Article
371-379
Continuous Solutions of Systems of Linear Difference-Functional Equations
Abstract
We establish conditions for the existence of continuous solutions for a class of linear systems of difference-functional equations, propose a method for the construction of solutions of this kind, and study the structure of the set of these solutions.
380-396
Robust Stabilization of Nonlinear Mechanical Systems
Abstract
We study the problems of robust stabilization and optimization of the equilibrium states of nonlinear mechanical systems. Sufficient conditions for the stabilization of a linear system with measured output feedback are formulated by means of the full-order state observers. The solution of the general problem of robust stabilization and the estimates of the quadratic performance criterion are presented for a family of nonlinear systems on examples of a one-link pendulum on a moving platform in the upper equilibrium position and a pendulum with flywheel control. The application of the obtained results is reduced to the solution of systems of linear matrix inequalities.
397-411
New Results on Periodic Solutions to Impulsive Nonautonomous Evolutionary Equations with Time Delays
Abstract
We obtain new results on periodic solutions for a class of nonautonomous impulsive evolutionary equations with time delays. Under suitable assumptions, such as the ultimate boundedness of the solutions of equations, we establish a theorem on periodic solutions to equations of this kind by using the Horn fixed-point theorem. At the end of the paper, we present an application to the case of nonautonomous impulsive partial differential equation with finite time delay.
412-425
Construction of Global Solutions of Partial Differential Equations with Deviating Arguments in the Time Variable
Abstract
A class of partial differential equations with deviating arguments in the time variable is investigated. We establish conditions under which it is possible to construct global solutions of these equations and describe the structure of these solutions and the algorithm used for their construction. We also consider some special cases and examples and prove the theorems substantiating the proposed method.
426-441
Variation Formulas for the Solution of Delay Differential Equations with Mixed Initial Conditions and Delay Perturbations
Abstract
Variation formulas are proved for the solution of nonlinear differential equations with constant delays. The essential novelty of the work is the effect of delay perturbations in the variation formulas. Mixed initial conditions mean that, at the initial time, some coordinates of the trajectory do not coincide with the corresponding coordinates of the initial function, whereas the other coordinates coincide. The variation formulas are used in the proof of necessary optimality conditions.
442-475
Oscillation Criteria for Some Second-Order Superlinear Differential Equations
Abstract
We study a class of second-order superlinear equations. New oscillations criteria are established by using a general class of parameter functions in the averaging techniques. We extend and improve the oscillation criteria of several authors. One of our results is based on the information for the whole half line and the other is based on the information on a sequence subintervals of the whole half line.
476-489
Exponential Dichotomy and Existence of Almost Periodic Solutions of Impulsive Differential Equations
Abstract
We establish conditions for the existence of piecewise continuous almost periodic solutions of a system of impulsive differential equations with exponentially dichotomous linear part. The robustness of exponential dichotomy and exponential contraction are investigated for linear systems with small perturbations of the right-hand sides and the points of impulsive action.
490-502
A New Hermite–Hadamard-Type Inequality and its Application to Quasi-Einstein Metrics
Abstract
We first establish a new generalization of the classical Hermite–Hadamard inequality for a real-valued convex function. Then the convexity of the matrix function g(A) = f(det A) is proved under certain conditions imposed on the function f and the matrix A: On this basis, we deduce a new Hermite–Hadamard-type inequality and finally present an application to the estimation of the volume of quasi-Einstein metrics.
503-519