An eigenvalue comparison theorem for second order self-adjoint differential equations
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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.
KeywordsBoundary Condition Differential Equation Special Consideration Differential System Comparison Theorem
- G. Birkhoff andS. MacLane,A Survey of Modern Algebra, Revised Edition, The MacMillan Co., New York (1953).Google Scholar
- O. Bolza,Lectures on the Calculus of Variations, University of Chicago Press, Chicago (1904).Google Scholar
- M. Morse,The Calculus ot Variations in the Large, American Mathematical Society (1934).Google Scholar