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The asymptotic form of the Titchmarsh–Weyl coefficient for a fourth order differential equation

Published online by Cambridge University Press:  14 November 2011

D. B. Hinton  and
J. K. Shaw
D. B. Hinton
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996–1300, U.S.A.
J. K. Shaw
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24061–4097, U.S.A.
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Synopsis

This paper considers the asymptotic form, as λ tends to infinity in sectors omitting the real axis, of the matrix Titchmarsh-Weyl coefficient M(λ) for the fourth order equation y(4) + q(x)y = λy, where q(x) is real and locally absolutely integrable. By letting M0(λ) denote the m-coefficient for the Fourier case y(4) = λy, the asymptotic formula M(λ) = M0(λ) + 0(1) is established.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 109 - 123
Copyright
Copyright © Royal Society of Edinburgh 1984

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