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Journal of Inequalities and Applications

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Open Access 01.12.2006 | Research Article

Eigenvalues of the -Laplacian and disconjugacy criteria

verfasst von: Pablo L. De Napoli, Juan P. Pinasco

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

We derive oscillation and nonoscillation criteria for the one-dimensional

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F37191/MediaObjects/13660_2005_Article_1589_IEq2_HTML.gif

-Laplacian in terms of an eigenvalue inequality for a mixed problem. We generalize the results obtained in the linear case by Nehari and Willett, and the proof is based on a Picone-type identity.

Vorheriger Artikel Extensions of the results on powers of -hyponormal and -hyponormal operators

Nächster Artikel Exponential stability in a scalar functional differential equation

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Allegretto W, Huang YX: A Picone's identity for the-Laplacian and applications. Nonlinear Analysis. Theory, Methods & Applications 1998,32(7):819–830. 10.1016/S0362-546X(97)00530-0MATHMathSciNetCrossRef

Anane A, Chakrone O, Moussa M: Spectrum of one dimensional-Laplacian operator with indefinite weight. Electronic Journal of Qualitative Theory of Differential Equations 2002,2002(17):1–11.MathSciNetMATH

Barrett JH: Oscillation theory of ordinary linear differential equations. Advances in Mathematics 1969,3(4):415–509. 10.1016/0001-8708(69)90008-5MATHMathSciNetCrossRef

Browder FE: Infinite dimensional manifolds and non-linear elliptic eigenvalue problems. Annals of Mathematics. Second Series 1965,82(3):459–477. 10.2307/1970708MATHMathSciNetCrossRef

Coppel WA: Disconjugacy, Lecture Notes in Mathematics. Volume 220. Springer, Berlin; 1971:iv+148.

del Pino M, Elgueta M, Manásevich R: Generalizing Hartman's oscillation result for. Houston Journal of Mathematics 1991,17(1):63–70.MATHMathSciNet

del Pino M, Manásevich R: Oscillation and nonoscillation for. Houston Journal of Mathematics 1988,14(2):173–177.MATHMathSciNet

Došlý O: Qualitative theory of half-linear second order differential equations. Mathematica Bohemica 2002,127(2):181–195.MATHMathSciNet

Došlý O, Peña S: A linearization method in oscillation theory of half-linear second-order differential equations. Journal of Inequalities and Applications 2005,2005(5):535–545. 10.1155/JIA.2005.535MATHMathSciNet

10.

Došlý O, Řehák P: Half-Linear Differential Equations. Elsevier, Amsterdam; 2005.MATH

11.

Elbert Á: Oscillation and nonoscillation theorems for some nonlinear ordinary differential equations. In Ordinary and Partial Differential Equations (Dundee, 1982), Lecture Notes in Math.. Volume 964. Springer, Berlin; 1982:187–212.CrossRef

12.

Fučík S, Nečas J: Ljusternik-Schnirelmann theorem and nonlinear eigenvalue problems. Mathematische Nachrichten 1972, 53: 277–289. 10.1002/mana.19720530123MATHMathSciNetCrossRef

13.

Jaroš J, Takaŝi K, Yoshida N: Picone-type inequalities for nonlinear elliptic equations and their applications. Journal of Inequalities and Applications 2001,6(4):387–404. 10.1155/S1025583401000236MATHMathSciNet

14.

Kim W: Disconjugacy and comparison theorems for second order linear systems. SIAM Journal on Mathematical Analysis 2002, 354: 4751–4767.

15.

Liapounov A: Problème Général de la Stabilité du Mouvement, Annals of Mathematics Studies. Volume 17. Princeton University Press, New Jersey; 1949. reprinted from Annales de la Faculté des Sciences de Toulouse 9 (1907), 203–474, translation of original paper published in Communications of the Society of Mathematics, Kharkow (1892) reprinted from Annales de la Faculté des Sciences de Toulouse 9 (1907), 203–474, translation of original paper published in Communications of the Society of Mathematics, Kharkow (1892)

16.

Mirzov JD: On some analogs of Sturm's and Kneser's theorems for nonlinear systems. Journal of Mathematical Analysis and Applications 1976,53(2):418–425. 10.1016/0022-247X(76)90120-7MATHMathSciNetCrossRef

17.

Nehari Z: Oscillation criteria for second-order linear differential equations. Transactions of the American Mathematical Society 1957,85(2):428–445. 10.1090/S0002-9947-1957-0087816-8MATHMathSciNetCrossRef

18.

Pinasco JP: Lower bounds for eigenvalues of the one-dimensional-Laplacian. Abstract and Applied Analysis 2004,2004(2):147–153. 10.1155/S108533750431002XMATHMathSciNetCrossRef

19.

Riddell RC: Nonlinear eigenvalue problems and spherical fibrations of Banach spaces. Journal of Functional Analysis 1975,18(3):213–270. 10.1016/0022-1236(75)90015-4MATHMathSciNetCrossRef

20.

Shere KD: Nonoscillation of second-order, linear differential equations with retarded argument. Journal of Mathematical Analysis and Applications 1973,41(2):293–299. 10.1016/0022-247X(73)90203-5MATHMathSciNetCrossRef

21.

Takaŝi K, Naito M: On the number of zeros of nonoscillatory solutions to half-linear ordinary differential equations involving a parameter. Transactions of the American Mathematical Society 2002,354(12):4751–4767. 10.1090/S0002-9947-02-03079-9MATHMathSciNetCrossRef

22.

Walter W: Sturm-Liouville theory for the radial-operator. Mathematische Zeitschrift 1998,227(1):175–185. 10.1007/PL00004362MATHMathSciNetCrossRef

23.

Willett D: Classification of second order linear differential equations with respect to oscillation. Advances in Mathematics 1969,3(4):594–623. 10.1016/0001-8708(69)90011-5MATHMathSciNetCrossRef

24.

Yoshida N: Nonoscillation of elliptic differential equations of second order. Hiroshima Mathematical Journal 1974, 4: 279–284.MATHMathSciNet

Titel: Eigenvalues of the-Laplacian and disconjugacy criteria
verfasst von: Pablo L. De Napoli
Juan P. Pinasco
Publikationsdatum: 01.12.2006
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/JIA/2006/37191

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