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# The Sturm-Lioville of the parameters of the boundary conditions

Author: ZhangMaoZhu
Tutor: HuangZhenYou
School: Nanjing University of Technology and Engineering
Course: Basic mathematics
Keywords: Sturm-Liouville problem Parametric boundary conditions Krein space Eigenvalue Characteristic function Oscillation Theory Eigenvalue ratio
CLC: O175.8
Type: Master's thesis
Year: 2007
Quote: 0

### Abstract

 This paper consider the boundary conditions contain the parameters of the Sturm-Liouville problem . The first part , we introduce some basic concepts such as positive is of Sturm - Liouville problems , boundary conditions containing the parameters of the problem in Krein space and Krein space definition and properties of a class of parameters of the boundary conditions of the Sturm-Liouville problem is described , and to prove it can constructed a Krein space of self-adjoint operators , and the spectrum of the point spectrum . The second part considers the first boundary condition is a linear function of the parameter , the second boundary condition for a rational function of the parameters of the Sturm-Liouville problem . We give the eigenvalue problem , asymptotic formula of the characteristic function and the characteristic function of oscillation theory , given the application instance . The third part , we discuss a class of parametric boundary conditions of the Sturm-Liouville problem , the first boundary condition for the Dirichlet boundary conditions , the second boundary condition for a linear function of the parameters of the eigenvalue . We are given the potential function q ≥ 0 , or q <0 when the eigenvalue ratio estimate , and noted that when the potential function q ≥ 0 , and the constant term of the linear function b ≤ 0 when all the eigenvalues ??are positive real numbers .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems