Differential Equations and Green's Functions

2005 ◽  
pp. 3-6
Keyword(s):  
Differential Equations ◽  
Green's Functions ◽  
Green’S Functions

ON A CERTAIN NONLOCAL POTENTIAL

1966 ◽  
Vol 44 (3) ◽  
pp. 629-636 ◽  
Author(s):  
V. de la Cruz ◽  
B. A. Orman ◽  
M. Razavy
Keyword(s):  
Differential Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Second Order ◽  
Numerical Results ◽  
Nonlocal Potential ◽  
Second Order Differential Equations ◽  
Nonlocal Potentials

A solvable example of a class of nonlocal potentials, whose kernels are related to Green's functions of second-order differential equations, is examined. This solvable example is applied to a few standard problems and, in particular, acceptable numerical results are obtained for p–p scattering in the 1S state.

POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 07 (04) ◽  
pp. 405-418 ◽  
Author(s):  
M. I. GIL'
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Green's Functions ◽  
Arbitrary Order ◽  
Green’S Functions ◽  
Higher Order ◽  
Volterra Integral Equations ◽  
Differential Delay

We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.

Time-Domain Poroelastic Green's Functions

2003 ◽  
Vol 11 (03) ◽  
pp. 491-501 ◽  
Author(s):  
Andrzej Hanyga
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Time Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Isotropic Case ◽  
The Time Domain ◽  
Singular Memory ◽  
Asymptotic Time

A method previously developed for asymptotic solution of systems of integro-differential equations with singular memory is applied to the determination of the time-domain asymptotic Green's function of Biot's poroelasticity. Asymptotic time-domain Green's functions are constructed in a neighborhood of the wavefronts. The general anisotropic medium as well as the isotropic case are considered.

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