Accession Number:

AD0257782

Title:

ASYMPTOTIC ESTIMATES FOR THE STURM-LIOUVILLE SPECTRUM

Descriptive Note:

Corporate Author:

NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s):

Report Date:

1961-02-01

Pagination or Media Count:

1.0

Abstract:

It is shown that the differential equation y x y 0 can, under suitable conditions, be solved by assuming a solution of the form y Ax sin x where x x 14 xx sin 2 xAx -Ax 2 2 xx cos2 x. Use of the first equation leads, when boundary conditions are applied, to asymptotic estimates of the eigenvalues. In particular, in the case of Hills equation, it is shown that the instability intervals vanish faster than any inverse power of k, k being the order of the corresponding eigenvalues, when x is an analytic function Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE