Green's function and comparison principles for first order periodic differential equations with piecewise constant arguments☆
TLDR
In this article, the expression of the Green's function related with a first order periodic differential equation with piecewise constant argument was obtained and comparison results for the treated linear operator were derived by studying the sign of the obtained Green's functions.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2004-03-15 and is currently open access. It has received 40 citations till now. The article focuses on the topics: Green's function & Green's function for the three-variable Laplace equation.read more
Citations
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Nonlinear boundary value problem of first order impulsive functional differential equations
Lijing Chen,Jitao Sun +1 more
TL;DR: In this paper, the authors discuss nonlinear boundary value problem for first order impulsive functional differential equations and establish several existence results by using the lower and upper solutions and monotone iterative techniques.
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On the reduction principle for differential equations with piecewise constant argument of generalized type
TL;DR: In this paper, a new type of differential equations with piecewise constant argument (EPCAG) was introduced, and the reduction principle in the theory of the stability of motion was proved for EPCAG.
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Periodic solutions of differential equations with a general piecewise constant argument and applications
Kuo-Shou Chiu,Manuel Pinto +1 more
TL;DR: In this paper, the existence of periodic solutions of a quasilinear differential equation with piecewise constant argument of generalized type was investigated and sufficient conditions were obtained for t he existence.
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Cauchy and Green matrices type and stability in alternately advanced and delayed differential systems
TL;DR: In this article, the authors studied DEPCAGs with piecewise constant argument of generalized (DEPCAG) type, i.e., the argument is a general step function and the play of the discrete part is always very important.
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On the almost automorphy of bounded solutions of differential equations with piecewise constant argument
Nguyen Van Minh,Tran Tat Dat +1 more
TL;DR: In this article, the authors give sufficient spectral conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form x ′ ( t ) = A x ( [ t ] ) + f ( t ), t ∈ R, where A is a bounded linear operator in X and f is an X -valued almost automorphic function.
References
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Retarded differential equations with piecewise constant delays
Kenneth L. Cooke,Joseph Wiener +1 more
TL;DR: In this article, the authors studied functional and functional differential equations and showed that functional equations are directly connected with difference equations of a discrete (for example, integer-valued) argument, the theory of which has been very intensively developed in the book and in numerous subsequent papers.
Book
Generalized Solutions of Functional Differential Equations
TL;DR: In this paper, a coexistence of analytic and distributional solutions for linear differential equations differential equations with piecewise continuous argument partial differential equations was studied. But the coexistence was not considered for functional differential equations.
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The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems
TL;DR: In this paper, the authors developed the monotone method in the presence of lower and upper solutions for the problem u (n) (t)=ƒ(t, u(t));u (i) (a)−u(i)(b)=λ i ∈ R ; i=0,..., n−1.
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Advanced differential equations with piecewise constant argument deviations
S. M. Shah,Joseph Wiener +1 more
TL;DR: In this article, the authors studied functional differential equations of advanced type with piecewise constant argument deviations and showed that they are closely related to impulse, loaded and especially to difference equations, and have the structure of continuous dynamical systems within intervals of unit length.
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A class of piecewise linear differential equations arising in biological models
Jean-Luc Gouzé,Tewfik Sari +1 more
TL;DR: In this paper, the authors investigate the properties of the solutions of a class of piecewise-linear differential equations, which are appropriate to model biological systems (e.g. genetic networks) in which there are switchlike interactions between the elements.