Related papers: Green function solution of generalised boundary va…
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary…
In this paper we consider a boundary value problem for fully fourth order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation…
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
A systematic construction of the Green's matrix for a second order, self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the…
In the paper the conditions are obtained providing existence and uniqueness of the regular solution of the boundary problem for class of the second order homogeneous operator-differential equation with singular coefficients. High term of…
We discuss solutions of the one-dimensional telegrapher's equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green's function.…
Nonlocal problems for higher-order elliptic operators in dihedral and plane angles are considered. The Green formula is obtained, which leads to adjoint problems that take the form of nonlocal transmission problems in dihedral and plane…
In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann-Stieltjes integral boundary condition. By using the spectral…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
In this paper we estimate norms of integral operator induced with Green function related to the Poisson equation in the unit ball with vanishing boundary data.
The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…
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 consider a class of nonlinear fractional differential equations involving Hilfer derivative with boundary conditions. First, we obtain an equivalent integral for the given boundary value problem in weighted space of…
We describe a new Maple package for treating boundary problems for linear ordinary differential equations, allowing two-/multipoint as well as Stieltjes boundary conditions. For expressing differential operators, boundary conditions, and…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
Boundary value problems (BVPs) play a central role in the mathematical analysis of constrained physical systems subjected to external forces. Consequently, BVPs frequently emerge in nearly every engineering discipline and span problem…
The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…
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…
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…