Indefinite sturm-liouville problems

Royal Society of Edinburgh - Proceedings A

Volumn 133, Issue 3, 2003, Pages 639-652

  Kong, Q ^a   Wu, H ^a   Zettl, A ^a   Moller M ^b  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544294101     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0308210500002584     Document Type: Article

References (22)

1. T. Ya. Azizov and I. S. Iohvidov. Linear operators in spaces with an indefinite metric (Wiley, 1989).
2. P. Binding and P. Browne. Form domains for sectorial operators related to generalized Sturm-Liouville problems. Q. J. Math. 50 (1999), 155-178.
3. P. Binding and H. Volkmer. Eigencurves for two-parameter Sturm-Liouville equations. SIAM Rev. 38 (1996), 27-48.
4. J. Bognar. Indefinite inner product spaces (Springer, 1974).
5. B. Čurgus and H. Langer. A Krein space approach to symmetric ordinary differential operators with an indefinite weight function. J. Diff. Eqns 79 (1989), 31-61.
6. W. N. Everitt and A. Zettl. Sturm-Liouville differential operators in direct sum spaces. Rocky Mt. J. Math. 16 (1986), 497-516.
7. S. Goldberg. Unbounded linear operators (New York: Dover, 1985).
8. I. S. Iohvidov, M. G. Krein and H. Langer. Introduction to the spectral theory of operators in spaces with an indefinite metric. Mathematische Forschung, vol. 9 (Berlin: Akademie, 1982).
9. T. Kato. Pertubation theory for linear operators (Springer, 1966).
10. Q. Kong, H. Wu and A. Zettl. Left-definite Sturm-Liouville problems. J. Diff. Eqns 177 (2001), 1-26.
11. M. G. Krein. The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications I. Mat. Sb. 20 (1947), 431-495. (In Russian.)
12. M. G. Krein. The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications II. Mat. Sb. 21 (1947), 365-404. (In Russian.)
13. A. B. Mingarelli. Indefinite Sturm-Liouville problems. Lecture Notes in Mathematics, vol. 964, pp. 519-528 (Springer, 1982).
14. M. Möller. On the essential spectrum of a class of operators in Hubert space. Math. Nachr. 194 (1998), 185-196.
15. M. Möller. On the unboundedness below of the Sturm-Liouville operator. Proc. R. Soc. Edinb. A 129 (1999), 1011-1015.
16. M. A. Naimark. Linear differential operators (New York: Ungar, 1968).
17. R. G. D. Richardson. Über die notwendigen und hinreichenden Bedingungen für das Bestehen eines Kleinschen Oszillationstheorems. Math. Ann. 83 (1910), 289-304.
18. R. G. D. Richardson. Theorems of oscillation for two linear differential equations of the second order with two parameters. Trans. Am. Math. Soc. 13 (1912), 22-34.
19. R. G. D. Richardson. Contributions to the study of oscillation properties of the solutions of linear differential equations of the second order. Am. J. Math. 40 (1918), 283-316.
20. A. Schneider and R. Vonhoff. Indefinite boundary eigenvalue problems in a Pontrjagin space setting. Res. Math. 35 (1999), 325-354.
21. H. Volkmer. Sturm-Liouville problems with indefinite weights and Everitt's inequality. Proc. R. Soc. Edinb. A 126 (1996), 1096-1112.
22. A. Zettl. Sturm-Liouville problems. In Spectral theory and computational methods of Sturm-Liouville problems, pp. 1-104 (New York: Dekker, 1997).