Cover Image

Method of local linear approximation in the theory of nonlinear impulsive systems

UDC 517.929 For nonlinear differential equations with impulsive perturbations, we formulate a general assertion concerning the existence of bounded solutions.&nbsp;&nbsp;With the help of this assertion, we establish necessary and sufficient conditions for the existence and uniqueness...

Full description

Saved in:

Bibliographic Details
Date:	2023
Main Authors:	Perestyuk , М. О., Slyusarchuk, V. Yu., Перестюк, М. О., Слюсарчук, В. Ю., Slyusarchuk, V.
Format:	Article
Language:	Ukrainian
Published:	Institute of Mathematics, NAS of Ukraine 2023
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/7347
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Method of local linear approximation in the theory of bounded solutions of nonlinear differential equations
by: Slyusarchuk, V. Yu., et al.
Published: (2009)

Method of local linear approximation for nonlinear discrete equations
by: Slyusarchuk, V. Yu., et al.
Published: (2019)

Method of local linear approximation in the theory of nonlinear impulsive systems
by: M. O. Perestiuk, et al.
Published: (2023)

Green–Samoilenko operator in the theory of invariant sets of nonlinear differential equations
by: Perestyuk, N. A., et al.
Published: (2009)

Theorems on instability of systems with respect to linear approximation
by: Slyusarchuk, V. E., et al.
Published: (1996)

A Criterion for the Existence of Almost Periodic Solutions of Nonlinear Differential Equations with Impulsive Perturbation
by: Slyusarchuk, V. Yu., et al.
Published: (2015)

Method of local linear approximation for nonlinear discrete equations
by: Yu. Sliusarchuk
Published: (2019)

Periodic solutions of nonlinear differential equations with pulse influence in a banach space
by: Perestyuk, N. A., et al.
Published: (1995)

General Theorems on the Existence and Uniqueness of Solutions of Impulsive Differential Equations
by: Slyusarchuk, V. E., et al.
Published: (2000)

Invertibility conditions for nonlinear autonomous differential operators in the space of functions bounded on the axis
by: Slyusarchuk, V. Yu., et al.
Published: (2021)

Periodic solutions of quasi-linear impulse systems in a critical case
by: Akhmetov , M. U., et al.
Published: (2025)

Some modern aspects of the theory of impulsive differential equations
by: Perestyuk, N. A., et al.
Published: (2008)

Exponential stability of invariant manifold for nonlinear impulsive multifrequency system
by: P. Feketa, et al.
Published: (2019)

Necessary and sufficient conditions for oscillation of solutions of nonlinear pulse systems with multiplicatively separated right-hand side
by: Slyusarchuk, V. Yu., et al.
Published: (1995)

Application of the Green–Samoilenko function and operator to the study of non-Lipschitz differential equations
by: Perestyuk , M. O., et al.
Published: (2021)

Investigations of the properties of solutions of impulsive differential systems in the linear approximation
by: Yu. A. Mitropolsky, et al.
Published: (2008)

Investigations of the properties of solutions of impulsive differential systems in the linear approximation
by: Mitropolsky, Yu.A., et al.
Published: (2008)

Linear differential-functional equations with absolutely unstable solutions
by: Slyusarchuk, V. Yu., et al.
Published: (2026)

Necessary and sufficient conditions for the invertibility of nonlinear differentiable maps
by: Slyusarchuk, V. Yu., et al.
Published: (2016)

Conditions for the existence and uniqueness of bounded solutions of nonlinear differential equations
by: Slyusarchuk, V. Yu., et al.
Published: (2009)

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations
by: Slyusarchuk, V. Yu., et al.
Published: (2010)

Almost Periodic Solutions of Nonlinear Equations that are not Necessarily Almost Periodic in Bochner’s Sense
by: Slyusarchuk, V. Yu., et al.
Published: (2015)

Conditions for the existence of almost periodic solutions of nonlinear differential equations in Banach spaces
by: Slyusarchuk, V. Yu., et al.
Published: (2013)

Conditions of existence of bounded and almost periodic solutions of nonlinear differential equation with perturbations of solutions
by: Slyusarchuk, V. Yu., et al.
Published: (2016)

Conditions for Almost Periodicity of Bounded Solutions of Nonlinear Differential Equations Unsolved with Respect to the Derivative
by: Slyusarchuk, V. Yu., et al.
Published: (2014)

Periodic solutions of nonlinear differential equations with pulse influence in a Banach space
by: Perestyuk, N.A., et al.
Published: (1995)

On the Favard theory without $H$ -classes for differential-functional equations in Banach spaces
by: Slyusarchuk, V. Yu., et al.
Published: (2019)

On Stability of Integral Sets of Impulsive Differential Systems
by: Perestyuk, N. A., et al.
Published: (2002)

Necessary and sufficient conditions for the absolute instability of solutions of linear differential-difference equations with self-adjoint operator coefficients
by: Slyusarchuk, V. Yu., et al.
Published: (2018)

Nonlinear difference equations with asymptotically stable solutions
by: Slyusarchuk, V. E., et al.
Published: (1997)

Nonlinear differential equations with asymptotically stable solutions
by: Slyusarchuk, V. E., et al.
Published: (1998)

Favard – Amerio theory for almost periodic functional-differential equations without the use of $H$-classes of these equations
by: Slyusarchuk, V. Yu., et al.
Published: (2017)

Global attractors of impulsive infinite-dimensional systems
by: Kapustyan, O. V., et al.
Published: (2016)

Averaging of set-valued impulsive systems
by: Perestyuk, N. A., et al.
Published: (2013)

Mechanical analogs of linear impulsive systems
by: Pryz, A. M., et al.
Published: (2011)

Necessary and sufficient conditions for the oscillation of solutions of nonlinear differential equations with pulse influence in a banach space
by: Slyusarchuk, V. E., et al.
Published: (1999)

On stability of linear impulse systems with switchings
by: V. I. Slynko, et al.
Published: (2016)

On the stability of a trivial invariant torus of one class of impulsive systems
by: Dudzyanyi, S. I., et al.
Published: (1998)

Problems of approximation theory in linear spaces
by: Stepanets, O. I., et al.
Published: (2006)

Differential convergence criteria for operator improper integrals and series
by: Slyusarchuk, V. Yu., et al.
Published: (2021)