Differential equations with state-dependent piecewise constant argument

Date

2010-06-01

Author

Akhmet, Marat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

243
views

0
downloads

A new class of differential equations with state-dependent piecewise constant argument is introduced. It is an extension of systems with piecewise constant argument. Fundamental theoretical results for the equations the existence and uniqueness of solutions, the existence of periodic solutions, and the stability of the zero solution are obtained. Appropriate examples are constructed.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/49257

Journal

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

DOI

https://doi.org/10.1016/j.na.2010.01.050

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Integral manifolds of differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-01-15) In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG). The existence of global integral manifolds of the quasilinear EPCAG is established when the associated linear homogeneous system has an exponential dichotomy. The smoothness of the manifolds is investigated. The existence of bounded and periodic solutions is considered. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Ap...
Stability of differential equations with piecewise constant arguments of generalized type Akhmet, Marat (Elsevier BV, 2008-02-15) In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367-383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and Sufficient conditions for stability of the zero Solution are ob...
Matrix measure approach to Lyapunov-type inequalities for linear Hamiltonian systems with impulse effect Kayar, Zeynep; Zafer, Ağacık (Elsevier BV, 2016-08-01) We present new Lyapunov-type inequalities for Hamiltonian systems, consisting of 2n-first-order linear impulsive differential equations, by making use of matrix measure approach. The matrix measure estimates of fundamental matrices of linear impulsive systems are crucial in obtaining sharp inequalities. To illustrate usefulness of the inequalities we have derived new disconjugacy criteria for Hamiltonian systems under impulse effect and obtained new lower bound estimates for eigenvalues of impulsive eigenva...
On the reduction principle for differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-12-01) In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297...
Integral criteria for oscillation of third order nonlinear differential equations AKTAŞ, MUSTAFA FAHRİ; Tiryaki, Aydın; Zafer, Ağacık (Elsevier BV, 2009-12-15) In this paper we are concerned with the oscillation of third order nonlinear differential equations of the form

Citation Formats

M. Akhmet, “Differential equations with state-dependent piecewise constant argument,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 4200–4210, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49257.