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Linear Multistep Methods for Functional Differential Equations [PDF]
Mathematics of Computation, 1987 The author discusses linear multistep methods for functional differential equations which are correct for the jumps in the derivatives of the solution. The asymptotic behavior of the global discretization error is discussed as well as the implementation of these methods in predictor- corrector mode with step changing strategy based on the estimation of
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Reduction of Linear Functional Systems using Fuhrmann's Equivalence
Sultan Qaboos University Journal for Science, 2016 Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns ...
Mohamed S. Boudellioua
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On periods of non-constant solutions to functional differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2017 We show that periods of solutions to Lipschitz functional differential equations cannot be too small. The problem on such periods is closely related to the unique solvability of the periodic value problem for linear functional differential equations ...
Eugene Bravyi
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Input-to-State Stability of Linear Stochastic Functional Differential Equations
Journal of Function Spaces, 2016 The purpose of the paper is to show how asymptotic properties, first of all stochastic Lyapunov stability, of linear stochastic functional differential equations can be studied via the property of solvability of the equation in certain pairs of spaces of
Ramazan Kadiev, Arcady Ponosov
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Electronic Journal of Qualitative Theory of Differential Equations, 2012 Some general conditions sufficient for unique solvability of the boundary-value problem for a system of linear functional differential equations of the second order are established.
Natalia Dilna
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CANONICAL APPROXIMATIONS IN IMPULSE STABILIZATION FOR A SYSTEM WITH AFTEREFFECT
Ural Mathematical Journal, 2023 For optimal stabilization of an autonomous linear system of differential equations with aftereffect and impulse controls, the formulation of the problem in the functional state space is used.
Yuri F. Dolgii
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POISSON PROBLEM FOR A LINEAR FUNCTIONAL DIFFERENTIAL EQUATION
Tambov University Reports. Series: Natural and Technical Sciences, 2016 The solvability, existence and positiveness of the Green function of the Poisson problem -∆uΩu y -u x r x,dy =ρf, u | Γ( Ω) =0 are showed. The spectral properties of corresponding eigenvalue problem are considered. Here Ω is an open set in R N and ΓΩ is the boundary of the Ω. For almost all x Ω, r x,∙ is a measure satisfying certain symmetry condition.
LABOVSKIY SERGEI MIKHAILOVICH +1 more
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On linear singular functional-differential equations in one functional space
Abstract and Applied Analysis, 2004 We use a special space of integrable functions for studying the Cauchy problem for linear functional-differential equations with nonintegrable singularities. We use the ideas developed by Azbelev and his students (1995).
Andrei Shindiapin
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Electronic Journal of Qualitative Theory of Differential Equations, 2000 The spectral set of an operator which is associated with linear autonomous functional differential equations is determined. The consequence is applied to study the admissibility of linear autonomous functional differential equations for the function ...
Satoru Murakami +2 more
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Distributional and entire solutions of linear functional differential equations
International Journal of Mathematics and Mathematical Sciences, 1982 A unified approach to the study of generalized-function and entire solutions to linear functional differential equations with polynomial coefficients is suggested.
Joseph Wiener
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