Open Access
Access granted
Subscription Access
Vol 243, No 3 (2019)
- Year: 2019
- Articles: 8
- URL: https://journal-vniispk.ru/1072-3374/issue/view/15037
Article
Existence and Attractivity Results for Hilfer Fractional Differential Equations
Abstract
We present some results on the existence of attracting solutions of some fractional differential equations of the Hilfer type. The results on the existence of solutions are applied to the Schauder fixed-point theorem. It is proved that all solutions are uniformly locally attracting.
347-357
Almost Periodic Solutions of the Lotka–Volterra Systems with Diffusion and Nonfixed Times of Pulsed Action
Abstract
We study the conditions of existence and asymptotic stability of strongly positive piecewise continuous almost periodic solutions of the Lotka–Volterra systems of differential equations with diffusion and nonfixed times of pulsed action.
358-380
Asymptotics of the Solutions of Second-Order Differential Equations with Regularly and Rapidly Varying Nonlinearities
Abstract
We establish conditions for the existence of a class of monotone solutions of the second-order differential equations with regularly and rapidly varying nonlinearities and the asymptotic representations of these solutions as t ↑ ω (ω ≤ + ∞).
381-408
Weakly Nonlinear Boundary-Value Problems for the Fredholm Integral Equations with Degenerate Kernels in Banach Spaces
Abstract
We consider weakly nonlinear boundary-value problems for the Fredholm integral equations with degenerate kernel in Banach spaces, establish necessary and sufficient conditions for the existence of solutions of these problems, and construct convergent iterative procedures for the determination of solutions of these boundary-value problems.
409-420
Schemes of Complete Averaging in the Problem of Optimal Control Over a Functional-Differential System
Abstract
For nonlinear controlled functional-differential systems, the possibility of applying of the method of averaging on a finite interval without the condition of constancy of the asymptotic control is proved and an algorithm for the construction of the corresponding controls over the original and averaged systems is proposed.
421-432
Asymptotics of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations
Abstract
By using the theory of polynomial matrix pencils, we construct the asymptotics of linearly independent solutions of homogeneous singularly perturbed system of linear differential equations of any order m with matrices at higher derivatives degenerating as a small parameter approaches zero. The general case is analyzed. In this case, the limit matrix pencil has several finite and infinite elementary divisors of both the same and different multiplicities. The corresponding asymptotic estimates are presented.
433-466
467-492
493-504