Singular left-definite Sturm-Liouville problems

Journal of Differential Equations

Volumn 206, Issue 1, 2004, Pages 1-29

  Kong, Q ^a   Wu, H ^a   Zettl, A ^a  

^a Illinois University   (United States)

Author keywords

Eigenfunctions; Eigenvalue inequalities; Eigenvalues; Left definite; Singular problems

Indexed keywords

EID: 4544261679     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.07.027     Document Type: Article

References (29)

1. P.B. Bailey W.N. Everitt A. Zettl The SLEIGN2 Sturm-Liouville code ACM Trans. Math. Software 21 2001 143-192
2. C. Bennewitz, W.N. Everitt, On the second-order left-definite boundary value problems, Lecture Notes in Mathematics, vol. 1032, 1983, Springer, Heidelberg, pp. 31-67
3. P.A. Binding P. Browne Asymptotics of eigencurves for second order ordinary differential equations, I J. Differential Equations 88 1990 30-45
4. P.A. Binding P. Browne R.H. Picard Corrigendum Spectral properties of two-parameter eigenvalue problems, II Proc. Roy. Soc. Edinburgh 115A 1990 87-90
5. P.A. Binding P.J. Browne Left-definite Strum-Liouville problems with eigenparameter dependent boundary conditions Differential Integral Equations 12 1999 167-182
6. P.A. Binding H. Volkmer Eigencurves for two parameter Sturm-Liouville equations SIAM Rev. 38 1996 27-48
7. B.M. Brown D.K.R. McCormack W.D. Evans M. Plum On the spectrum of second order differential operators with complex coefficients Proc. Roy. Soc. London 455 A 1999 1234-1257
8. B. Curgus H. Langer A Krein space approach to symmetric ordinary differential operators with an indefinite weight function J. Differential Equations 79 1989 31-61
9. K. Daho H. Langer Sturm-Liouville Operators with an indefinite weight function Proc. Roy. Soc. Edinburgh 78A 1997 161-191
10. N. Dunford J.T. Schwartz Linear Operators vol. II 1963 Wiley New York
11. E. Eastham, Q. Kong, H. Wu, A. Zettl, Inequalities among eigenvalues of Sturm-Liouville problems, J. Inequalities Appl. 3 (1999) 25-43
12. W.N. Everitt, Some remarks on a differential expression with an indefinite weight function, in: E.M. de Jager (Ed.), Proceedings of the Conference in Spectral Theory and Asymptotics of Differential Equations, Scheveningen, 1973, North-Holland Mathematics Studies, vol. 13, 1974, pp. 13-28.
13. W.N. Everitt Some remarks on the strong limit-point condition of second-order linear differential expressions Casopsis Pro Pestovani Matematiky 111 1986 137-145
14. H.G. Kaper M.K. Kwong A. Zettl Singular Sturm-L problems with nonnegative and indefinite weights Monatsheft fuer Mathematik 97 1984 177-189
15. Q. Kong M. Moller H. Wu A. Zettl Indefinite Sturm-Liouville problems Proc. Roy. Soc. Edinburgh Sect. A 133 2003 639-652
16. Q. Kong H. Wu A. Zettl Inequalities among eigenvalues of singular Sturm-Liouville problems Dynam. Systems Appl. 8 1999 517-531
17. Q. Kong H. Wu A. Zettl Left-definite Sturm-Liouville problems J. Differential Equations 177 2001 1-26
18. M.K. Kwong A. Zettl Discreteness conditions for the spectrum of ordinary differential operators J. Differential Equations 40 1981 53-70
19. L. Littlejohn R. Wellman A theory of left-definite self-adjoint operators with applications to differential equations J. Differential Equations 181 2002 280-339
20. H.-D. Niessen A. Schneider Linksdefinite singulaere kanische eigenwertproblems I J. Reine Angew. Math. 281 1976 13-52
21. H.-D. Niessen A. Schneider Linksdefinite singulaere kanische eigenwertproblems II J. Reine Angew. Math. 289 1977 62-84
22. H.-D. Niessen A. Zettl Singular Sturm-Liouville problems The Friedrichs extension and comparison of eigenvalues Proc. London Math. Soc. 64 1992 545-578
23. A. Pleijel Complementary remarks about the limit-point and limit-circle theory Arkiv för Mathematik 8 1971 45-47
24. A.R. Sims Secondary conditions for linear differential operators of the second order J. Math. Mech. 6 1957 247-285
25. R. Vonhoff A left-definite study of legendre's differential equation and of the fourth-order legendre type differential equation Results Math. 37 2000 155-196
26. R. Vonhoff, Spektraltheoretische untersuchung linksdefiniter differeentialgleichungen im singulaeren fall, Dissertation, Universitat Dortmund, 1995
27. J. Weidmann Spectral Theory of Ordinary Differential Operators Lecture Notes in Mathematics vol. 1258 1987 Springer Berlin
28. H. Weyl Ueber gewoehnliche Differentialgleichungen mit Singularitaeten und die zugehoerigen Entwicklungen willkuerlicher Funftionen Math. Ann. 68 1910 220-269
29. A. Zetatl, Sturm-Liouville problems, Spectral theory and computational methods of Sturm-Liouville problems (Knoxville, TN, 1996), Lecture Notes in Pure and Applied Mathematics, vol. 191, Dekker, New York, 1997, pp. 1-104