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Spectral asymptotics for Sturm-Liouville equations with indefinite weight |
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| Authors: | Paul A. Binding Patrick J. Browne Bruce A. Watson |
| Affiliation: | Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4 ; Mathematical Sciences Group, Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N 5E6 ; Department of Mathematics, University of the Witwatersrand, Private Bag 3, P O WITS 2050, South Africa |
| Abstract: | The Sturm-Liouville equation ![begin{displaymath}-(py')' + qy =lambda ry text{rm on} [0,l]end{displaymath}](http://www.ams.org/tran/2002-354-10/S0002-9947-02-03023-4/gif-abstract0/img1.gif){kind=small} is considered subject to the boundary conditions   We assume that  is positive and that  is piecewise continuous and changes sign at its discontinuities. We give asymptotic approximations up to  for  , or equivalently up to  for  , the eigenvalues of the above boundary value problem. |
| Keywords: | Eigenvalue asymptotics indefinite weight turning point |
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