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Vol 243, No 3 (2019)

Article

Existence and Attractivity Results for Hilfer Fractional Differential Equations

Abbas S., Benchohra M., Henderson J.

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.

Journal of Mathematical Sciences. 2019;243(3):347-357
pages 347-357 views

Almost Periodic Solutions of the Lotka–Volterra Systems with Diffusion and Nonfixed Times of Pulsed Action

Dvornyk A.V., Tkachenko V.I.

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.

Journal of Mathematical Sciences. 2019;243(3):358-380
pages 358-380 views

Asymptotics of the Solutions of Second-Order Differential Equations with Regularly and Rapidly Varying Nonlinearities

Evtukhov V.M., Kolun N.P.

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 tω (ω ≤ + ∞).

Journal of Mathematical Sciences. 2019;243(3):381-408
pages 381-408 views

Weakly Nonlinear Boundary-Value Problems for the Fredholm Integral Equations with Degenerate Kernels in Banach Spaces

Zhuravlev V.F.

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.

Journal of Mathematical Sciences. 2019;243(3):409-420
pages 409-420 views

Schemes of Complete Averaging in the Problem of Optimal Control Over a Functional-Differential System

Kichmarenko O.D.

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.

Journal of Mathematical Sciences. 2019;243(3):421-432
pages 421-432 views

Asymptotics of the General Solution of a Linear Singularly Perturbed System of Higher-Order Differential Equations with Degenerations

Pafyk S.P.

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.

Journal of Mathematical Sciences. 2019;243(3):433-466
pages 433-466 views

Non-Keplerian Behavior and Instability of Motion of Two Bodies Caused by the Finite Velocity of Gravitation

Slyusarchuk V.Y.

Abstract

It is shown that the motion of two bodies described with regard for the finite velocity of gravitation does not obey the Kepler laws and that this motion is unstable.

Journal of Mathematical Sciences. 2019;243(3):467-492
pages 467-492 views

Thin-Film Flows on a Solid Sphere

Taranets R.M.

Abstract

By using the Arzela–Ascoli theorem, we prove the existence of strong solutions of the equation of thin-film flow on a solid sphere in weighted Sobolev spaces.

Journal of Mathematical Sciences. 2019;243(3):493-504
pages 493-504 views