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On eigencurves of elliptic boundary value problems

Published online by Cambridge University Press:  14 November 2011

P. A. Binding ,
P. J. Browne ,
Y. X. Huang  and
R. H. Picard
P. A. Binding
Affiliation:
Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
P. J. Browne
Affiliation:
Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
Y. X. Huang
Affiliation:
Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
R. H. Picard
Affiliation:
Department of Mathmatical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, U.S.A
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Synopsis

Let T be a selfadjoint uniformly elliptic partial differential operator on a bounded domain in Rn, and let S be a (possibly indefinite) L∞ multiplication operator. Estimates of the form σλ + o(λ) and σλ + β + o(1) are sought for the eigenvalues μ(λ) of λS – T as λ→ ±∞. A necessary and sufficient condition is also obtained for existence of linear eigencurves, i.e. μ(λ) = σλ + β.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 161 - 171
Copyright
Copyright © Royal Society of Edinburgh 1991

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