On Fundamental Solution for Autonomous Linear Retarded Functional Differential Equations
Mathematics, 2020 This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix; and the Laplace ...
Clement McCalla
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Existence of Nonnegative Solutions of Linear Autonomous Functional Differential Equations
Mathematics, 2020 It is shown that if we exclude the existence of nontrivial small solutions, then a linear autonomous functional differential equation has a nontrivial nonnegative solution if and only if it has a nonnegative eigenfunction.
Mihály Pituk
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Remark to transformations of linear differential and functional-differential equations [PDF]
Czechoslovak Mathematical Journal, 2000 summary:For linear differential and functional-differential equations of the $n$-th order criteria of equivalence with respect to the pointwise transformation are ...
Tryhuk, Václav
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On the Cauchy problem for linear hyperbolic functional-differential equations [PDF]
Czechoslovak Mathematical Journal, 2001 summary:We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type.
Šremr, Jiří +2 more
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Theory of Functional Connections Applied to Linear Discontinuous Differential Equations
MathematicsThis article introduces two numerical methods based on the Theory of Functional Connections (TFC) for solving linear ordinary differential equations that involve step discontinuities in the forcing term. The novelty of the first proposed approach lies in
Trent White, Daniele Mortari
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The Optimization of Trajectories of Linear Functional Differential Equations [PDF]
SIAM Journal on Control, 1970 Our aim in this paper is to examine a number of fundamental questions in the theory of optimal control of processes monitored by certain general systems of linear functional differential equations with finite memories. In our model the controls may appear in a very general nonlinear functional manner which permits us to consider retardations of a ...
Banks, H. T., Jacobs, Marc Q.
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Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
Discrete Dynamics in Nature and Society, 2021 Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general ...
Yunfei Li, Shoufu Li
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On the Control of a Linear Functional-Differential Equation with Quadratic Cost [PDF]
SIAM Journal on Control, 1970 Riccati-like linear functional differential equation with quadratic cost, analyzing feedback control solution existence and ...
Kushner, H. J., Barnea, D. I.
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Fractal and Fractional, 2023 Contrary to the initial-value problem for ordinary differential equations, where the classical theory of establishing the exact unique solvability conditions exists, the situation with the initial-value problem for linear functional differential ...
Natalia Dilna
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General exact solvability conditions for the initial value problems for linear fractional functional differential equations [PDF]
, 2023 summary:Conditions on the unique solvability of linear fractional functional differential equations are established.
Dilna, Natalia
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