On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications

doi:10.1088/1674-1056/20/10/100202

Abstract In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechanics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.

Keywords: operator matrix eigenvalue problem eigenvector root vector completeness

Received: 27 January 2011
Revised: 05 June 2011
Accepted manuscript online:

PACS:	02.30.Tb	(Operator theory)
	02.30.Jr	(Partial differential equations)
	46.25.-y	(Static elasticity)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11061019 and 10962004), the Chunhui Program of Ministry of Education of China (Grant No. Z2009-1-01010), the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2010MS0110 and 2009BS0101), and the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University.

Cite this article:

Wang Hua(王华), Alatancang (阿拉坦仓), and Huang Jun-Jie(黄俊杰) On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications 2011 Chin. Phys. B 20 100202

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