On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems
type: Item
instance of: scholarly article
title: On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems
zbMATH Open document ID: 1545.34028
DOI: 10.2989/16073606.2023.2277841
author: Elgiz Bairamov
author: K. Tas
author: Ekin Ugurlu
published in: Quaestiones Mathematicae
publication date: 2024-06-01T00:00:00Z
review text: The authors consider the following equation\N\[\N-\left( py^{\prime}\right) ^{\prime}+qy=\lambda\omega y,~x\in\left[ a,b\right) ,\N\]\Nwith a singular left-definite Hamiltonian system\N\[\NJY^{\prime}=\left( \lambda A+B\right) Y,\N\]\Nwhere \(J,A,B\) are \(r\times r\) matrices such that \(J\) is a constant matrix satisfying \(J^{\ast}=-J,\) \(A\) and \(B\) are locally integrable matrix-functions on \(\left[ a,b\right) \) satisfying \(A^{\ast}=A\) and \(B^{\ast}=B.\) They study the characteristic-matrix theory of the system and some results on its Dirichlet-integrable solutions.
reviewed by: Fatma Hıra
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 7858260
MaRDI profile type: Publication
cites work: Discrete and continuous boundary problems
cites work: A generalisation of Niessen's limit-circle criterion
cites work: Q3944887
cites work: Green's function method and the first-order linear differential equation
cites work: Scattering problems of impulsive Schrödinger equations with matrix coefficients
cites work: Q5848416
cites work: Singular differential equations. I: The even order case
cites work: Integrable-Square, Analytic Solutions of Odd-Order, Formally Symmetric, Ordinary Differential Equations
cites work: Q5570370
cites work: Q3950841
cites work: Parameterization of the M(λ) function for a Hamiltonian system of limit circle type
cites work: Hamiltonian systems of limit point or limit circle type with both endpoints singular
cites work: Q5526276
cites work: On Ordinary Differential Equations of any Even Order and the Corresponding Eigenfunction Expansions
cites work: 1.—On Square-integrable Solutions of Symmetric Systems of Differential Equations of Arbitrary Order.
cites work: Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation
cites work: $M(\lambda )$ Theory for Singular Hamiltonian Systems with One Singular Point
cites work: Left definite theory for second order differential operators with mixed boundary conditions
cites work: Left‐Definite Regular Hamiltonian Systems
cites work: Q5569399
cites work: On a singular Sturm-Liouville problem in the theory of molecular vibrations
cites work: The supersymmetric quantum mechanics theory and Darboux transformation for the Morse oscillator with an approximate rotational term
cites work: Resolvent operator and spectrum of new type boundary value problems
cites work: Some remarks about the limit point and limit circle theory
cites work: Q4056367
cites work: An efficient wavelet based spectral method to singular boundary value problems
cites work: S-hermitesche Rand-Eigenwertprobleme. III
cites work: Q5838785
cites work: Discrete left-definite Hamiltonian systems
cites work: Left-definite Hamiltonian systems and corresponding nested circles
cites work: On the rate of the convergence of the characteristic values of an integral operator associated with a dissipative fourth order differential operator in lim-4 case with finite transmission conditions
cites work: On Dirichlet-integrable solutions of left-definite Hamiltonian systems
cites work: Singular left-definite Hamiltonian systems in the Sobolev space
cites work: Some Remarks on Left-Definite Hamiltonian Systems in the Regular Case
cites work: A Vector-Matrix Formulation for Formally Symmetric Ordinary Differential Equations with Applications to Solutions of Integrable Square
cites work: Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen.
cites work: Q5698659
description: scientific article; zbMATH DE number 7858260