scholarly journals Relativistic Two-Body Problem: Existence and Uniqueness of Two-Sided Solutions to Functional-Differential Equations of Motion

1996 ◽  
Vol 3 (3-4) ◽  
pp. 379-384
Author(s):  
V.I. Zhdanov
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
Two Body Problem ◽  
Functional Differential

scholarly journals RADIATIVE DAMPING AND FUNCTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2627-2638 ◽  
Author(s):  
SUVRAT RAJU ◽  
C. K. RAJU
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
General Technique ◽  
Covariant Model ◽  
Maxwell Electrodynamics ◽  
Functional Differential ◽  
The One ◽  
Radiative Damping

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

On Bounded Solutions of Systems of Linear Functional Differential Equations

1999 ◽  
Vol 6 (5) ◽  
pp. 429-440
Author(s):  
R. Hakl
Keyword(s):  
Differential Equations ◽  
Real Axis ◽  
Existence And Uniqueness ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Functional Differential

Abstract Sufficient conditions of the existence and uniqueness of bounded on real axis solutions of systems of linear functional differential equations are established.

scholarly journals Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
T. E. Govindan
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Local Lipschitz Condition ◽  
Functional Differential ◽  
Special Case ◽  
Partial Functional Differential Equation

This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

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