Cover Image

Theorems on instability of systems with respect to linear approximation

We study the problem of instability of solutions of differential equations with a stationary linear part and a nonstationary nonlinear compact part in a Banach space.

Saved in:

Bibliographic Details
Date:	1996
Main Authors:	Slyusarchuk, V. E., Слюсарчук, В. Е.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 1996
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/5254
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

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

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

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)

Refinement of Kneser theorem on zeros of solutions of the equation $y" + p(x)y = 0$
by: Slyusarchuk, V. E., et al.
Published: (1996)

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 in the theory of nonlinear impulsive systems
by: Perestyuk , М. О., et al.
Published: (2023)

Conditions for Instability of an Invariant Toroidal Manifold of a Discrete Dynamical System in a Banach Space
by: Slyusarchuk, V. V., et al.
Published: (2001)

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)

Equations in a Hilbert space whose solution sets are invariant with respect to a group isomorphic to a one-parameter group of unitary operators
by: Slyusarchuk, V. Yu., et al.
Published: (2020)

Generalization of the Mukhamadiev theorem on the invertibility of functional operators in the space of bounded functions
by: Slyusarchuk, V. Yu., et al.
Published: (2008)

Generalization of the Kneser theorem on zeros of solutions of the equation $y" + p (t) y = 0$
by: Slyusarchuk, V. Yu., et al.
Published: (2007)

Strengthening of the Kneser theorem on zeros of solutions of the equation $u″ + q(t)u = 0$ using one functional equation
by: Slyusarchuk, V. Yu., et al.
Published: (2010)

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

Essentially unstable solutions of difference equations
by: Slyusarchuk, V. E., et al.
Published: (1999)

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)

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)

Theory of Potential with Respect to Consistent Kernels; Theorem on Completeness and Sequences of Potentials
by: Zorii, N. V., et al.
Published: (2004)

Investigation of systems of differential equations with delays and constraints imposed on the delays and derivatives of the solutions
by: Slyusarchuk, V. Yu., 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)

Investigation of a nonlinear difference equation in a Banach space in a neighborhood of a quasiperiodic solution
by: Samoilenko, A. M., et al.
Published: (1997)

Theorem of differentiation of the energy of a multiatomic system with respect to atomic coordinates (Part I)
by: I. O. Marushko
Published: (2014)

Theorem of differentiation of the energy of a multiatomic system with respect to atomic coordinates (part I)
by: I. O. Marushko
Published: (2014)

Generalization of Abel and Dirichlet signs
by: Slyusarchuk, V. Yu., et al.
Published: (2020)

Optimization of approximate integration of set-valued functions monotone with respect to inclusion
by: Babenko, V. V., et al.
Published: (2011)

Asymptotics of the fundamental system of solutions of a linear functional-differential equation with respect to a parameter
by: Radzievskii, G. V., et al.
Published: (1995)

Klee Theorem for Linearly Convex Sets
by: Momot, I. V., et al.
Published: (2002)

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

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

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

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)

Differential Equations with Absolutely Unstable Trivial Solutions
by: Slyusarchuk, V. Yu., et al.
Published: (2013)

Existence and exponential stability of periodic solution for fuzzy BAM neural networks with periodic coefficient
by: Slyusarchuk, V. Yu., et al.
Published: (2011)

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

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

Denseness of the set of Cauchy problems with nonunique solutions in the set of all Cauchy problems
by: Slyusarchuk, V. Yu., et al.
Published: (2012)

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)

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)

Almost periodic and Poisson stable solutions of difference equations in metric spaces
by: Slyusarchuk, V. Yu., et al.
Published: (2015)