Spectrum of a class of fourth order left-definite differential operators  

作　　者：GAO Yun-lan SUN Jiong 

机构地区：[1]Dept. of Math., Inner Mongolia Univ. of Tech., Hohhot 010051, China. [2]Dept. of Math., Inner Mongolia Univ., Hohhot 010021, China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2008年第1期51-56,共6页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(10561005);the Doctor's Discipline Fund of the Ministry of Education of China(20040126008)

摘　　要：The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…The spectrum of a class of fourth order left-definite differential operators is studied. By using the theory of indefinite differential operators in Krein space and the relationship between left-definite and right-definite operators, the following conclusions are obtained： if a fourth order differential operator with a self-adjoint boundary condition that is left-definite and right-indefinite, then all its eigenvalues are real, and there exist countably infinitely many positive and negative eigenvalues which are unbounded from below and above, have no finite cluster point and can be indexed to satisfy the inequality …≤λ-2≤λ-1≤λ-0〈0〈λ0≤λ1≤λ2≤…

关 键 词：left-definite differential operator right-definite differential operator Krein space spectrum eigenvalue. 

分 类 号：O29[理学—应用数学]