Non-Self-Adjoint Boundary Eigenvalue Problems
( Volume 192 )
Publication series ：Volume 192
Author： Mennicken R.;Möller M.
Publisher： Elsevier Science
Publication year： 2003
E-ISBN: 9780080537733
P-ISBN(Paperback): 9780444514479
P-ISBN(Hardback): 9780444514479
Subject： O175.1 Ordinary Differential Equations;O241 数值分析
Language： ENG
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Description
This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalent
to a first order system, the main techniques are developed for systems. Asymptotic fundamental
systems are derived for a large class of systems of differential equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.
The contour integral method and estimates of the resolvent are used to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections, variou
Chapter