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Exponential Dichotomies, the Fredholm Alternative, and Transverse Homoclinic Orbits in Partial Functional Differential Equations [PDF]

open access: yesJournal of Dynamics and Differential Equations, 2005
In this paper we investigate the transversality of homoclinic orbits in partial functional differential equations. We first discuss the exponential dichotomies for linear operator equations.
Shigui Ruan   +2 more
exaly   +2 more sources

Partial functional differential equations and Conley index

Journal of Differential Equations, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carbinatto, M. C., Rybakowski, K. P.
openaire   +2 more sources

Partial averaging of functional differential equations

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2003
Develops a framework for averaging functional differential equations (FDEs) with two time scales. Averaging is performed on the fast time system, while slow time is 'frozen.' This creates an averaged equation which is slowly time-varying, hence the terminology of partial averaging.
B. Lehman, S.P. Weibel
openaire   +1 more source

On state-dependent delay partial neutral functional–differential equations

Applied Mathematics and Computation, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo Hernández Morales   +1 more
openaire   +2 more sources

Comparison method of partial functional differential equations and its application

Applied Mathematics and Computation, 2002
Here, the initial value problem \[ \frac{du}{dt} = Au + f(t,u_t), \quad t \geq 0, \qquad u = \varphi (t), \quad t \in [-r,0], \] is considered on the real Banach space \(X\), where \(u_t = u(t + \theta)\), \(-r \leq \theta \leq 0\), and \(A\) is a linear operator on \(X\).
Mengxing He, Zhuoling Ou, Anping Liu
openaire   +2 more sources

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