Related papers: Insight of the Green's function as a defect state …
This article addresses the construction and analysis of the Green's function for the Neumann boundary value problem associated with the operator $-\Delta + a$ on a smooth bounded domain $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) with $a\in…
In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
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…
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, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
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 the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. We consider the elliptic system in a Lipschitz domain with mixed boundary conditions.…
We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.
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…
On a bounded domain $\Omega \subset \mathbb{R}^N$, $N\geq 2$, we consider existence, uniqueness and "regularity" issues for the Green function $G_\lambda$ of the quasi-linear operator $u \to -\Delta_p u-\lambda |u|^{p-2}u$ with $1<p \leq…
In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…
Two approaches are developed for the study of the bound states of a one-dimensional Dirac equation with the potential consisting of $N$ $\delta$-function centers. One of these uses the Green's function method. This method is applicable to a…
We investigate a first boundary value problem for a second-order partial differential equation involving the Prabhakar fractional derivative in time. Using structural properties of the Prabhakar kernel and generalized Mittag-Leffler…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
We provide explicit formulas for the Green function of an elliptic PDE in the infinite strip and the half-plane. They are expressed in elementary and special functions. Proofs of uniqueness and existence are also given.
We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…
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…
In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or -- equivalently -- a…