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Geometric aspects of Sturm-Liouville problems II. Space of boundary conditions for left-definiteness


Authors: Kevin Haertzen, Qingkai Kong, Hongyou Wu and Anton Zettl
Journal: Trans. Amer. Math. Soc. 356 (2004), 135-157
MSC (2000): Primary 34B24, 34B09; Secondary 34L05, 34L15
DOI: https://doi.org/10.1090/S0002-9947-03-03028-9
Published electronically: August 21, 2003
MathSciNet review: 2020027
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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 $n$-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: https://doi.org/10.1090/S0002-9947-03-03028-9
Keywords: Regular Sturm-Liouville problems, left-definiteness, spaces of boundary conditions
Received by editor(s): November 16, 2001
Published electronically: August 21, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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