Search results for " integral equation."

Numerical treatment of the long-range Coulomb potential with Berggren bases

2010

The Schrodinger equation incorporating the long-range Coulomb potential takes the form of a Fredholm equation whose kernel is singular on its diagonal when represented by a basis bearing a continuum of states, such as in a Fourier-Bessel transform. Several methods have been devised to tackle this difficulty, from simply removing the infinite-range of the Coulomb potential with a screening or cut function to using discretizing schemes which take advantage of the integrable character of Coulomb kernel singularities. However, they have never been tested in the context of Berggren bases, which allow many-body nuclear wave functions to be expanded, with halo or resonant properties within a shell…

A scalar Volterra derivative for the PoU-integral

2005

Some coincidence and periodic points results in a metric space endowed with a graph and applications

2015

The purpose of this paper is to obtain some coincidence and periodic points results for generalized $F$-type contractions in a metric space endowed with a graph. Some examples are given to illustrate the new theory. Then, we apply our results to establishing the existence of solution for a certain type of nonlinear integral equation.

Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation

2014

Abstract We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an α - ψ -type contractive mapping and then for a generalized β -type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results.

Hybrid coincidence and common fixed point theorems in Menger probabilistic metric spaces under a strict contractive condition with an application

2014

Abstract We prove some coincidence and common fixed point theorems for two hybrid pairs of mappings in Menger spaces satisfying a strict contractive condition. An illustrative example is given to support the genuineness of our extension besides deriving some related results. Then, we establish the corresponding common fixed point theorems in metric spaces. Finally, we utilize our main result to obtain the existence of a common solution for a system of Volterra type integral equations.

Krasnosel'skiĭ-Schaefer type method in the existence problems

2019

We consider a general integral equation satisfying algebraic conditions in a Banach space. Using Krasnosel'skii-Schaefer type method and technical assumptions, we prove an existence theorem producing a periodic solution of some nonlinear integral equation.

FREDHOLM THEORY FOR DEGENERATE PSEUDODIFFERENTIAL OPERATORS ON MANIFOLDS WITH FIBERED BOUNDARIES

2001

We consider the calculus Ψ*,* de(X, deΩ½) of double-edge pseudodifferential operators naturally associated to a compact manifold X whose boundary is the total space of a fibration. This fits into the setting of boundary fibration structures, and we discuss the corresponding geometric objects. We construct a scale of weighted double-edge Sobolev spaces on which double-edge pseudodifferential operators act as bounded operators, characterize the Fredholm elements in Ψ*,* de(X) by means of the invertibility of an appropriate symbol map, and describe a K-theoretical formula for the Fredholm index extending the Atiyah–Singer formula for closed manifolds. The algebra of operators of order (0, 0) i…

Lévy flights in an infinite potential well as a hypersingular Fredholm problem.

2016

We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schr\"odinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain $D$, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numer…

Common fixed point results on quasi-Banach spaces and integral equations

2013

In this paper we obtain fixed and common fixed point theorems for self-mappings defined on a closed and convex subset C of a quasi-Banach space. We give also a constructive method for finding the common fixed points of the involved mappings. As an application we obtain a result of the existence of solutions of integral equations.

Hollow system with fin. Transient Green function method combination for two hollow cylinders

2017

In this paper we develop mathematical model for three dimensional heat equation for the system with hollow wall and fin and construct its analytical solution for two hollow cylindrical sample. The method of solution is based on Green function method for one hollow cylinder. On the conjugation conditions between both hollow cylinders we construct solution for system wall with fin. As result we come to integral equation on the surface between both hollow cylinders. Solution is obtained in the form of second kind Fredholm integral equation. The generalizing of Green function method allows us to use Green function method for regular non-canonical domains.