Solution of a Homogeneous Version of Love Type Integral Equation in Different Asymptotic Regimes (original) (raw)

On an Integral Equation with the Riemann Function Kernel

Axioms

This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations, and the representation of solutions of singular Sturm–Liouville and Shrödinger equations. A special integral equation is derived and formulated using the Riemann function of a singular hyperbolic equation. In the paper, the existence of a unique solution to this equation is proven by the method of successive approximations. The results can be applied, for example, to representations of solutions to Sturm–Liouville equations with singular potentials, such as Bargmann and Miura potentials, and similiar. The treatment of problems with such potentials are very important in mathematical physics, and inverse, scattering and related problems. The estimates received do not contain any undefined constants, and for transmutation kernels all est...

On a class of integral equations having application in quantum dynamics

Journal of Physics A: Mathematical and Theoretical, 2007

A class of Fredholm integral equations of the second kind is studied, with kernel separable outside the basic interval (a, b). Using theorems of matrix algebra, the solution for x outside (a, b) is found in terms of the Fredholm determinants in a simple and compact form. As a particular case, the quantum propagator for one-dimensional problems is obtained.

Convolution Integral Equations with Two Kernels

Journal of Mathematical Extension, 2015

In this paper, we consider the integral equation of convolution type with some conditions which has two kernels. At first we change this integral equation to a simple operator form and then, we approximate it by Topelitzian and Hankelian series.

The solvability and explicit solutions of two integral equations via generalized convolutions

Journal of Mathematical Analysis and Applications, 2010

This paper presents the necessary and sufficient conditions for the solvability of two integral equations of convolution type; the first equation generalizes from integral equations with the Gaussian kernel, and the second one contains the Toeplitz plus Hankel kernels. Furthermore, the paper shows that the normed rings on L 1 (R d) are constructed by using the obtained convolutions, and an arbitrary Hermite function and appropriate linear combination of those functions are the weight-function of four generalized convolutions associating F and F. The open question about Hermitian weight-function of generalized convolution is posed at the end of the paper.

On integral equations of the first kind with logarithmic kernels

Journal of Integral Equations and Applications, 1988

The existence-uniqueness of the solution and its behaviour for one-dimensional integral equations of the first kind with logarithmic kernels are investigated. The analysis is based on the transfinite diameter or logarithmic capacity and spaces deriving from Fourier series. The uniqueness results apply to any closed bounded subset of the plane. The other results apply to open arcs, polygons and other regions with piecewise-smooth boundaries.

A collocation method for solving some integral equations in distributions

Journal of Computational and Applied …, 2011

A collocation method is presented for numerical solution of a typical integral equation Rh := D R(x, y)h(y)dy = f (x), x ∈ D of the class R, whose kernels are of positive rational functions of arbitrary selfadjoint elliptic operators defined in the whole space R r , and D ⊂ R r is a bounded domain. Several numerical examples are given to demonstrate the efficiency and stability of the proposed method.