Related papers: General Representation of Nonlinear Green's Functi…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
During the past three decades, the advantageous concept of the Green's function has been extended from linear systems to nonlinear ones. At that, there exist a rigorous and an approximate extensions. The rigorous extension introduces the…
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…
In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particular, we show that if the nonlinear term possesses a special…
We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
In this paper we obtain the explicit expression of the Green's function related to a general $n$ order differential equation coupled to non-local linear boundary conditions. In such boundary conditions, a $n$ dimensional parameter…
We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…
We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
An explicit perturbative solution to all orders is given for a general class of nonlinear differential equations. This solution is written as a sum indexed by rooted trees and uses the Green function of a linearization of the equations. The…
In this paper we develop a way of obtaining Green's functions for partial differential equations with linear involutions by reducing the equation to a higher-order PDE without involutions. The developed theory is applied to a model of heat…
General formula for causal Green's function of linear differential operator of given degree in one variable is given according to coefficient functions of differential operator as a series of integrals. The solution also provides analytic…
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary conditions, giving an explicit Green's function for it. Then we…
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
An analytic iteration sequence based on the extension of the BLUES (Beyond Linear Use of Equation Superposition) function method to partial differential equations (PDEs) with second-order time derivatives is studied. The original…