Related papers: Green's function related to a n order linear diffe…

In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…

Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or…

We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that the Green's function is BMO in the domain and establish…

This paper aims to investigate the existence and uniqueness of solutions for a sixth order differential equation involving nonlocal and integral boundary conditions. Firstly, we obtain the properties of the relevant Green's functions. The…

This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…

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…

This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…

This paper is a revised version of the original paper of same title--published in Applied Mathematics Letters 89--containing some corrections and clarifications to the original text. We derive non-singular Green's functions for the…

A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…

We show that a Green function solution can be given for a class of non-homogeneous nonlinear systems having relevance in quantum field theory. This in turn means that a quantum field theory in the strong coupling limit can be formulated and…

We consider a problem of finding vanishing at infinity $C^1([0,\oo))$-solutions to non-homogeneous system of linear ODEs which has the pole of first order at $x=0$. The resonant case where the corresponding homogeneous problem has…

This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives with nonlocal boundary conditions. We investigate the Green function and some of its…

We provide an elementary derivation of the Green's function for Poisson's equation with Neumann boundary data on balls of arbitrary dimension, which was recently found in [Sadybekov et al., Eurasian Math. J. 7(2):100-105, 2016]. The…

One-dimensional $\delta^{'}$-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent…

In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary…

We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…

Using pointwise semigroup techniques of Zumbrun--Howard and Mascia--Zumbrun, we obtain sharp global pointwise Green function bounds for noncharacteristic boundary layers of arbitrary amplitude. These estimates allow us to analyze linearized…

A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is…

We construct Green's function for second order elliptic operators of the form $Lu=-\nabla \cdot (\mathbf{A} \nabla u + \boldsymbol{b} u)+ \boldsymbol c \cdot \nabla u+ du$ in a domain and obtain pointwise bounds, as well as Lorentz space…

We construct Green's functions for second order parabolic operators of the form $Pu=\partial_t u-{\rm div}({\bf A} \nabla u+ \boldsymbol{b}u)+ \boldsymbol{c} \cdot \nabla u+du$ in $(-\infty, \infty) \times \Omega$, where $\Omega$ is an open…