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A note on a paper of Atkinson concerning the asymptotics of an eigenvalue problem with interior singularity

Published online by Cambridge University Press:  14 November 2011

B.J. Harris
B.J. Harris
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115–2888, U.S.A.
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Synopsis

In [2] Atkinson considers the asymptotic form of the eigenvalues of the linear differentialequation

where a < 0 < b and y satisfies appropriate conditions at a andb. In particular Atkinson considers where q is singular at 0. In this case q(x) = xK, his results cover the case l ≦ K < . We extend Atkinson's results to cover more singular q, in the power case 1 ≦K <

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 1-2 , 1988 , pp. 63 - 71
Copyright
Copyright © Royal Society of Edinburgh 1988

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References

1Atkinson, F. V. and Fulton, C. T.. Asymptotics of eigenvalues for problems on a finite interval with one limit circle singularity I. Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 51–70.CrossRefGoogle Scholar
2Atkinson, F. V.. Asymptotics of an eigenvalue problem involving an interior singularity (preprint).Google Scholar
3Everitt, W. N. and Zettl, A.. Sturm Liouville differential operations in direct sum spaces. Rocky Mountain J. Math. 16 (1986), 497–516.CrossRefGoogle Scholar
4Harris, B. J.. On the oscillation of solutions of linear differential equations. Mathematika 31 (1984), 214–226.CrossRefGoogle Scholar