On a computer assisted proof of the existence of eigenvalues below the essential spectrum of the Sturm-Liouville problem

Journal of Computational and Applied Mathematics

Volumn 125, Issue 1-2, 2000, Pages 385-393

  Brown, B M ^a   McCormack, D K R ^a   Zettl, A ^b  

^a CARDIFF UNIVERSITY   (United Kingdom)

^b NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; DIGITAL ARITHMETIC; EIGENVALUES AND EIGENFUNCTIONS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

STURM-LIOUVILLE PROBLEMS;

THEOREM PROVING;

EID: 0034509268     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00481-7     Document Type: Article

References (11)

1. G. Alefeld, J. Herzberger, Introduction to interval computations, Academic Press, New York, 1983.
2. P.B. Bailey, W.N. Everitt, J. Weidman, A. Zettl, Regular approximations of singular Sturm-Liouville problems, Results Math. 23 (1993) 3-22.
3. B.M. Brown, M.S.P. Eastham, D.K.R. McCormack, Spectral concentration and rapidly decaying potentials, J. Comput. Appl. Math. 81 (1997) 333-348.
4. B.M. Brown, M.S.P. Eastham, D.K.R. McCormack, Resonances and analytic continuation for exponentially decaying Sturm-Liouville potentials, 1999, to appear.
5. B.M. Brown, W.D. Evans, V.G. Kirby, M. Plum, Safe numerical bounds for the Titchmarsh-Weyl m(λ)-function, Math. Proc. Camb. Phil. Soc. 113 (1993) 583-599.
6. B.M. Brown, D.K.R. McCormack, M. Marletta, On computing enclosures for the eigenvalues of Sturm-Liouville problems, Math. Nach. 213 (1999) 17-33.
7. B. Brown, D. McCormack, A. Zettl, On the existence of an eigenvalue below the essential spectrum, Proc. Roy. Soc. London A 455 (1999) 2229-2234.
8. M.S.P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh, 1973.
9. R. Lohner, Einschliessung der Lösung gewöhnlicher Anfangs- und Randwertaufgaben und Anwendungen, Doctoral Thesis, Universität Karlsruhe, 1988.
10. H. Siedentop, A generalization of Rouché's theorem with application to resonances, in: Resonances (Lertorpet, 1987), Springer, Berlin, 1989, pp. 77-85.
11. J. Weidmann, in: Spectral theory of ordinary differential operators, Lecture Notes in Mathematics, Vol. 1258, Springer, Berlin, 1987.