Abstract
We study the approximation of the discrete and continuous spectrum of singular left-definite Sturm-Liouville problems with eigenvalues of regular problems on truncated intervals.
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A.A. Abramov, K. Balla and N. Konyukhova, Stable initial manifolds and singular boundary value problems for systems of ordinary differential equations. Comput. Math. Banach Center Publications 13, 319–351 (1984).
F.V. Atkinson and D. Jabon, Indefinite Sturm-Liouville problems, in ’Proceedings of the Focused Research Program on Spectral Theory and Boundary Value Problems, Vol. II’ (H. Kaper, M.-K. Kwong and A. Zettl, eds.) pp. 31-45, Argonne National Laboratory (1988)
F.V. Atkinson and A. Mingarelli, Asymptotics of the number of zeros of the eigenvalues of general weighted Sturm-Liouville problems, J. Reine Angew. Math. 375/376, 380–393 (1987).
P.B. Bailey, W.N. Everitt, J. Weidmann and A. Zettl, Computing eigenvalues of singular Sturm-Liouville problems. Results in Mathematics 23, 3–22 (1993).
P.B. Bailey, W.N. Everitt, and A. Zettl, Regular approximation of singular Sturm-Liouville problems. Results in Mathematics 20, (1991), 391–423.
C. Bennewitz and W.N. Everitt, On second order left-definite boundary value problems, Uppsala University Department of Mathematics Report 1982, pp. 1-38.
P. Binding and P. Browne, Asymptotics of eigencurves for second order ordinary differential equations, I, J. Diff. Eq. 88, 30–45 (1990).
P. Binding and H. Volkmer, Eigenvalues for two-parameter Sturm-Liouville equations, SIAM Review 38, 27–48 (1996).
B.M. Brown and M. Marietta, Spectral inclusion and spectral exactness for elliptic PDEs on exterior domains. To appear in IMA J. Numer. Analysis (2004).
A. Constantin, A general weighted Sturm-Liouville problem, Ann. Scuola Norm. Sup. Pisa 24, 767–782 (1997).
B. Curgus and H. Langer, A Krein space approach to symmetric ordinary differential operators with an indefinite weight function, J. Diff. Eq. 79, 31–61 (1989).
B. K. Daho and H. Langer, Sturm-Liouville operators with an indefinite weight function, Proc. Roy. Soc. Edinburgh A78, 161–191 (1977).
Q. Kong, M. Möller, H. Wu and A. Zettl, Indefinite Sturm-Liouville Problems. Proc. Roy. Soc. Edinburgh Sect. A133 (2003), no. 3, 639–652.
Q. Kong, H. Wu and A. Zettl, Left-definite Sturm-Liouville problems. J. Differential Equations 177 (2001), no. 1, 1–26.
Q. Kong, H Wu and A. Zettl, Singular left-definite Sturm-Liouville problems. Preprint (2003).
P.A. Markowich, Eigenvalue problems on infinite intervals. Mathematics of Computation 39, 421–444 (1982).
M. Marietta and A. Zettl, Floquet theory for left-definite Sturm-Liouville problems. Preprint (2004).
G. Stolz and J. Weidmann, Approximation of isolated eigenvalues of general singular ordinary differential operators. Results in Mathematics 28, 345–358 (1995).
A. Zettl, Sturm-Liouville problems, Proceedings of the 1996 Knoxville Barrett Conference 191 (1997), 1-104, edited by D.B. Hinton and P. Shaefer, Marcel Dekker.
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An erratum to this article is available at http://dx.doi.org/10.1007/BF03323022.
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Marietta, M., Zettl, A. Spectral exactness and spectral inclusion for singular left-definite Sturm-Liouville problems. Results. Math. 45, 299–308 (2004). https://doi.org/10.1007/BF03323384
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DOI: https://doi.org/10.1007/BF03323384