Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
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
230
views
0
downloads
Cite This
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
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.