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Geometric aspects of Sturm-Liouville problems II. Space of boundary conditions for left-definiteness
Author(s):
Kevin
Haertzen;
Qingkai
Kong;
Hongyou
Wu;
Anton
Zettl
Journal:
Trans. Amer. Math. Soc.
356
(2004),
135-157.
MSC (2000):
Primary 34B24, 34B09;
Secondary 34L05, 34L15
Posted:
August 21, 2003
MathSciNet review:
2020027
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Abstract:
For a given regular Sturm-Liouville equation with an indefinite weight function, we explicitly describe the space of left-definite selfadjoint boundary conditions. The description only uses one value of a fundamental solution of the matrix form of the equation. As a consequence we show that this space has the shape of a solid consisting of two cones sharing a common base.
References:
-
- 1.
- M.Eastham, Q.Kong, H.Wu and A.Zettl: Inequalities among eigenvalues of Sturm-Liouville problems. J. Inequalities and Appl. 3 (1999), 25-43. MR 2000k:34132
- 2.
- W.Everitt, M.Möller and A.Zettl: Discontinuous dependence of the n-th Sturm-Liouville eigenvalue. ``General Inequalities" ed. C.Bandle, W.Everitt, L.Losonszi and W.Walter, 145-150. Birkhäuser, 1997. MR 98f:34033
- 3.
- Q.Kong, H.Wu and A.Zettl: Geometric aspects of Sturm-Liouville problems, I. Structures on spaces of boundary conditions. Proc. Royal Soc. Edinburgh 130A (2000), 561-589. MR 2001e:34042
- 4.
- Q.Kong, H.Wu and A.Zettl: Dependence of the
 -th Sturm-Liouville eigenvalue on the problem. J. Differential Equations 156 (1999), 328-354. MR 2000k:34045 - 5.
- Q.Kong, H.Wu and A.Zettl: Left-definite Sturm-Liouville problems. J. Differential Equations 177 (2001), 1-26.
- 6.
- A.Mingarelli: A survey of the regular weighted Sturm-Liouville problem-the non-definite case. ``International Workshop on Applied Differential Equations", 109-137. World Scientific, Singapore, 1986. MR 88e:34005
- 7.
- H.Niessen and A.Zettl: Singular Sturm-Liouville problems: the Friedrichs extension and comparison of eigenvalues. Proc. London Math. Soc. 64 (1992), 545-578. MR 93e:47060
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Additional Information:
Kevin
Haertzen
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
Qingkai
Kong
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
Hongyou
Wu
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
Anton
Zettl
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115
DOI:
10.1090/S0002-9947-03-03028-9
PII:
S 0002-9947(03)03028-9
Keywords:
Regular Sturm-Liouville problems,
left-definiteness,
spaces of boundary conditions
Received by editor(s):
November 16, 2001
Posted:
August 21, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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