An eigenvalue comparison theorem for second order self-adjoint differential equations

Summary This paper is concerned with a comparison of the eigenvalues for pairs of self-adjoint differential systems which arise from a single ordinary second-order differential equation. The sistems differ in the boundary conditions which are imposed, and it is these boundary conditions which will draw most of the attention. The principal results obtained deal with predicting alternation of the eigenvalues for two such systems from the boundary conditions alone, without special consideration of the differential equation. This paper is part of a thesis submitted to Carnegie Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The author wishes to express his thanks to the thesis director, ProfessorAllan D. Martin Jr. Presented to the American Mathematical Society November 17, 1962.