A variational approach to asymptotic spectrum of multiparameter eigenvalue problems in Hilbert space

Abstract

This thesis deals with the investigation of the asymptotic spectrum of a multiparameter problem in Hilbert space.Our discussion is based on estimates for eigenvalues derived froin the minimum-maximum principle, this thesis includes three chapters.The first chapter entitled: A development of multiparameter spectral theory. In this chapter we presents a general introduction to multiparameter spectral theory, the definitions and the basic results which be needed in our study.The second chapter entiteld: Asymptotic spectrum of multiparameter eigenvalue problems, this chapter is concerned with the asymptotic spectrum of multiparameter eigenvalue problem under definiteness conditions.The third chapter entitled: The multiparameter Sturm-Liouville problem. In this chaper we shall consider as an ,application, a multiparameter Sturm-Liouville problem.