Rayleigh quotient and minimazation principle for eigenvalues

In this thesis we study the Rayleigh quotient and minimization principle for eigenvalues. The thesis consist of four sections.In the first section a brief explanation has been given about the theoretical importance and some physical applications of the thema. the second section devoted to the history of the problem under consideration . In the third section we give the basic definitions and results used in this thesis.The last section we investigate some important spectral properties of a new type Sturm-Liouville problems,the main feature of which is the nature of boundary conditions, imposed particularly, we prove theorems about Rayleigh quotient and minimization principle for the eigenvalues.