Indefinite Eigenvalue problems with several singular points and turning points

Mathematische Nachrichten

Volumn 229, Issue , 2001, Pages 51-71

  Eberhard, Walter ^b   Freiling, Gerhard ^a   Wilcken Stoeber, Kerstin ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b NONE

Author keywords

Eigenfunction expansions; Indefinite spectral problems; Turning points; Weight function

Indexed keywords

EID: 0035661403     PISSN: 0025584X     EISSN: None     Source Type: Journal    
DOI: 10.1002/1522-2616(200109)229:1<51::AID-MANA51>3.0.CO;2-4     Document Type: Article

References (26)

1. ATKINSON, F. V., and MINGARELLI, A. B.: Asymptotics of the Number of Zeros and of the Eigenvalues of General Weighted Sturm-Liouville Problems, J. Reine Angew. Math. 375/376 (1987), 380-393
2. CURGUS, B., and LANGER, H.: A Krein-Space Approach to Symmetric Ordinary Differential Operators with an Indefinite Weight Function, J. Diff. Equ. 79 (1989), 31-61
3. DAHO, K., and LANGER, H.: Sturm-Liouville Operators with an Indefinite Weight Function, Proc. Roy. Soc. Edinburgh 78 A (1977), 161-191
4. DIJKSMA, A., GOHBERG, I., KAASHOEK, M. A., and MENNICKEN, R. (Eds.): Contributions to Operator Theory in Spaces with an Indefinite Metric, The Heinz Langer anniversary volume on the occasion of his 60th birthday, Operator Theory: Advances and Applications 106 (1998), Birkhaeuser, Basel
5. DORODNICYN, A. A.: Asymptotic Laws of Distribution of the Characteristic Values for Certain Special Forms of Differential Equations of the Second Order, Amer. Math. Soc. Translations 16 (1960), 1-101
6. EBERHARD, W., and FREILING, G.: The Distribution of the Eigenvalues for Second Order Eigenvalue Problems in the Presence of an Arbitrary Number of Turning Points, Results Math. 21 (1992), 24-41
7. EBERHARD, W., and FREILING, G.: An Expansion Theorem for Eigenvalue Problems with Several Turning Points, Analysis 13 (1993), 301-308
8. EBERHARD, W., FREILING, G., and SCHNEIDER, A.: Connection Formulas for Second Order Differential Equations with a Complex Parameter and Having an Arbitrary Number of Turning Points, Math. Nachr. 165 (1994), 205-229
9. FEDORYUK, M. V.: Asymptotic Analysis, Springer-Verlag, Berlin, 1993
10. FREILING, G., and YURKO, V.: Inverse Spectral Problems for Differential Equations on the Half-Line with Turning Points, Journal of Differential Equations 154 (1999), 419-453
11. LANGER, R. E.: The Boundary Problem Associated with a Differential Equation in Which the Coefficient of the Parameter Changes Sign, Trans. Amer. Math. Soc. 31 (1929), 1-24
12. LANGER, R. E.: On the Zeros of Exponential Sums and Integrals, Bull. Am. Math. Soc. 37 (1931), 213-239
13. LANGER, R. E.: On the Asymptotic Solutions of Ordinary Differential Equations, with an Application to the Bessel Functions of Large Order, Trans. Amer. Math. Soc. 33 (1931), 23-64
14. LANGER, R. E.: On the Asymptotic Solutions of Ordinary Differential Equations, with Reference to the Stokes' Phenomenon about a Singular Point, Trans. Amer. Math. Soc. 37 (1935), 397-416
15. LANGER, R. E.: The Asymptotic Solutions of a Linear Differential Equation of the Second Order with Two Turning Points, Trans. Amer. Math. Soc. 90 (1959), 113-142
16. MCHUGH, J.: An Historical Survey of Ordinary Linear Differential Equations with a Large Parameter and Turning Points, Arch. Hist. Exact. Sc. 7 (1970), 277-324
17. NAIMARK, M. A.: Linear Differential Operators, Part I, Frederick Ungar Publishing Co., 1967
18. OLVER, F. W. J.: Asymptotics and Special Functions, Acad. Press, New York, 1974
19. SCHNEIDER, A., and VONHOFF, R.: Indefinite Boundary Eigenvalue Problems in a Pontrjagin Space Setting, Result. Math. 35 (1999), 325-354
20. SCHRÖDER, M.: On the Asymptotic Distribution of the Eigenvalues of Singular Sturm-Liouville Problems with an Indefinite Weight Function, Results in Mathematics 32 (1997), 338-351
21. STAKUN, A. A.: Properties of a Differential Operator with a Multiple lining Point, Diff. Equ. 23 (1987), 667-671
22. TAMARKIN, J.: Some General Problems of the Theory of Ordinary Linear Differential Equations and Expansion of an Arbitrary Function in Series of Fundamental Functions, Math. Z. 27 (1928), 1-54
23. WASOW, W.: Linear Turning Point Theory, Springer-Verlag, Berlin, 1985
24. WILCKEN-STOEBER, K.: Über eine Klasse indefiniter Eigenwertprobleme zweiter Ordnung mit einer beliebigen Zahl von Nullstellen und Polen in der Gewichtsfunktion, Dissertation, Cuvillier Verlag Göttingen, 1998
25. ZYABLOV, A. A.: On the Basis Properties of the Eigenfunctions of a Model Problem with an Indefinite Weight, Mat. Zametki 54 (1993), 149-151 (Translation: Math. Notes 54 (1993), 1079-1080)
26. ZYABLOV, A. A.: On the Basis Properties of the Eigenfunctions of a Model Problem with an Indefinite Weight, Mat. Zametki 54 (1993), 149-151 (Translation: Math. Notes 54 (1993), 1079-1080)