How to solve the equation \(AuBu+Cu=f\).
type: Item
instance of: scholarly article
title: How to solve the equation \(AuBu+Cu=f\).
zbMATH Open document ID: 1051.47009
DOI: 10.1016/S0096-3003(01)00264-8
author: Chun-li Li
author: Minggen Cui
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The authors discuss the problem of solving the initial value problem \[ AuBu+Cu=f, \quad u(0)=1 \tag{1} \] where \(f, u\in W(\Omega)\), \(A,B,C\in L(W(\Omega))\), where \(W(\Omega)\) is the reproducing kernel space on the subset \(\Omega\) of \(\mathbb{R}^1\) and \(L(W(\Omega))\) is the space of continuous linear operators from \(W(\Omega)\) into \(W(\Omega)\). The authors use the method to transform a one-dimensional nonlinear operator equation into a two-dimensional linear operator equation. To achieve these results, they firstly discuss the problem how to solve a continuous linear operator equation in a separable Hilbert space. If the solution exists, there is given the representation and approximation of the minimal normal solution of the equation and formula are obtained. Further on, there is given a factorization method and characteristic value method to solve equation (1).
reviewed by: Muhib Lohaj
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 1861280
zbMATH Keywords: operator equation
zbMATH Keywords: reproducing kernel
zbMATH Keywords: nonlinear operator
MaRDI profile type: Publication
cites work: Theory of Reproducing Kernels
cites work: Q4726775
cites work: Linear integral equations
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description: scientific article; zbMATH DE number 1861280