Differential Equations and Green's Functions

2005 ◽  
pp. 3-6
1966 ◽  
Vol 44 (3) ◽  
pp. 629-636 ◽  
Author(s):  
V. de la Cruz ◽  
B. A. Orman ◽  
M. Razavy

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.


2009 ◽  
Vol 07 (04) ◽  
pp. 405-418 ◽  
Author(s):  
M. I. GIL'

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.


2003 ◽  
Vol 11 (03) ◽  
pp. 491-501 ◽  
Author(s):  
Andrzej Hanyga

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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