Accession Number:

AD0734678

Title:

Energy Methods in Self-Adjoint Eigenvalue Problems. 1. Variational Theory of the Spectrum

Descriptive Note:

Research rept.

Corporate Author:

POLYTECHNIC INST OF BROOKLYN NY DEPT OF AEROSPACE ENGINEERING AND APPLIED MECHANICS

Personal Author(s):

Report Date:

1971-09-01

Pagination or Media Count:

72.0

Abstract:

An essentially self-contained elementary account, from a unified variational point of view, is given of the theory of self-adjoint eigenvalue problems with discrete spectra, governed by linear differential equations of the form My lambda Ny. The theory is directly relevant for the various types of approximate energy methods applied in such problems. Included herein are statements and proofs of the variational, minimum, and maximum-minimum characterization of the eigenvalues in all modes. Theorems based on both the Rayleigh quotient and the energy quotient, including the role of natural boundary conditions, are developed. In addition, existence proofs, and discussion and proofs of completeness in both the N-norm and M-norm are given. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE