Applications of Cone Theory to Boundary Value Problems
Abstract
This Thesis is concerned with the existence and comparison of eigenvalues for the eigenvalue problem (-1) exp(n-1)Lu = lambda P(t)u, Tu = 0, where Tu = 0 are appropriate boundary conditions at points in the interval (a,b) . Here u(t) is an m-column vector function, P(t) is a continuous m x m matrix function on (a,b) and Lu = u(exp n) + p1(t)u(exp(n-1) +...+ Pn(t). Assume that the corresponding scalar equation Ly = 0 is right disfocal on (a,b). Existence and comparison results are gotten by using several abstract theorems from cone theory in a Banach space. We first consider the boundary value problem u(exp(n) + r(t)u = 0, u(exp i) (a) = 0, i = 0,1,...,k-1 and u(exp(i sub j)(b) = 0, j = 1, 2,...,n-k. Using comparison theorems for Green's functions due to Peterson and Ridenhour we are able to apply cone theory to get the existence and uniqueness of an eigenvector in a cone. Further, we can give comparison results between the smallest positive eigenvalues of different eigenvalue problems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1990
- Accession Number
- ADA220939
Entities
People
- Gerald Diaz
Organizations
- Air Force Institute of Technology