Integral manifolds of differential equations with piecewise constant argument of generalized type

Download

index.pdf

Date

2007-01-15

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

302
views

100
downloads

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. Appropriate illustrating examples are given.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/40273

Journal

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

DOI

https://doi.org/10.1016/j.na.2005.11.032

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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...
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...
Differential equations with state-dependent piecewise constant argument Akhmet, Marat (Elsevier BV, 2010-06-01) 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.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01) In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
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, “Integral manifolds of differential equations with piecewise constant argument of generalized type,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 367–383, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40273.