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

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2007-01-15

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Akhmet, Marat

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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

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Department of Mathematics, Article

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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...
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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.