Fold completeness of a system of root vectors of a system of unbounded polynomial operator pencils in Banach spaces.Ⅱ.Application

作     者：YAKUBOV Yakov 

作者机构：Raymond and Beverly Sackler Faculty of Exact SciencesSchool of Mathematical SciencesTel-Aviv University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2013年第56卷第1期

页      面：105-122页

核心收录：

学科分类：080902[工学-电路与系统] 07[理学] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the Israel Ministry of Absorption 

主　　题：fold completeness discrete spectrum regular problems eigenvalues root functions 

摘      要：This paper is a continuation of the author＇s paper in 2009, where the abstract theory of fold com- pleteness in Banach spaces has been presented. Using obtained there abstract results, we consider now very general boundary value problems for ODEs and PDEs which poIynomially depend on the spectral parameter in both the equation and the boundary conditions. Moreover, equations and boundary conditions may con- rain abstract operators as well. So, we deal, generally, with integro-differential equations, functional-differential equations, nonlocal boundary conditions, multipoint boundary conditions, integro-differential boundary condi- tions. We prove n-fold completeness of a system of root functions of considered problems in the corresponding direct sum of Sobolev spaces in the Banach Lq-framework, in contrast to previously known results in the Hilbert L2-framework. Some concrete mechanical problems are also presented.