Discreteness and simplicity of the spectrum of a quasilinear Sturm-Liouville-type problem on an infinite interval
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- by Pavel Drábek and Alois Kufner PDF
- Proc. Amer. Math. Soc. 134 (2006), 235-242 Request permission
Abstract:
We present sufficient conditions on the coefficients to get the discreteness and simplicity of the spectrum of a quasilinear Sturm-Liouville-type problem on an infinite interval. This condition appears to be necessary and sufficient for the compact embedding of certain weighted spaces. Our result generalizes those which are known from linear theory.References
- M.Cuesta: On the Fučík Spectrum of the Laplacian and the p-Laplacian. In: Proceedings of Seminar in Differential Equations (P. Drábek, ed.), Univ. of West Bohemia Pilsen (2000), 67-96.
- Ondřej Došlý, Oscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 28 (1998), no. 3, 507–521. MR 1657543
- O. Došlý: Oscillation Theory of Linear Differential and Difference Equations. In: Proceedings of Seminar in Differential Equations (P. Drábek, ed.), Univ. of West Bohemia Pilsen (2002), 7-71.
- P. Drábek and A. Kufner, Note on spectra of quasilinear equations and the Hardy inequality, Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday. Vol. 1, 2, Kluwer Acad. Publ., Dordrecht, 2003, pp. 505–512. MR 2060230
- Pavel Drábek and Stephen B. Robinson, Resonance problems for the $p$-Laplacian, J. Funct. Anal. 169 (1999), no. 1, 189–200. MR 1726752, DOI 10.1006/jfan.1999.3501
- Pavel Drábek and Stephen B. Robinson, On the generalization of the Courant nodal domain theorem, J. Differential Equations 181 (2002), no. 1, 58–71. MR 1900460, DOI 10.1006/jdeq.2001.4070
- Á. Elbert, A half-linear second order differential equation, Qualitative theory of differential equations, Vol. I, II (Szeged, 1979), Colloq. Math. Soc. János Bolyai, vol. 30, North-Holland, Amsterdam-New York, 1981, pp. 153–180. MR 680591
- B. Opic and A. Kufner, Hardy-type inequalities, Pitman Research Notes in Mathematics Series, vol. 219, Longman Scientific & Technical, Harlow, 1990. MR 1069756
- Andrzej Szulkin, Ljusternik-Schnirelmann theory on $\textit {C}^1$-manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), no. 2, 119–139 (English, with French summary). MR 954468, DOI 10.1016/S0294-1449(16)30348-1
Additional Information
- Pavel Drábek
- Affiliation: Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic
- Email: pdrabek@kma.zcu.cz
- Alois Kufner
- Affiliation: Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic
- Email: kufner@math.cas.cz
- Received by editor(s): February 25, 2004
- Received by editor(s) in revised form: August 30, 2004
- Published electronically: June 13, 2005
- Additional Notes: This research was supported by the Grant Agency of the Czech Republic, grant No. 201/03/0671, and by the Grant Agency of the Academy of Sciences of the Czech Republic, grant No. A1019305.
- Communicated by: Carmen C. Chicone
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 235-242
- MSC (2000): Primary 34L05, 47E05, 34B40
- DOI: https://doi.org/10.1090/S0002-9939-05-07958-X
- MathSciNet review: 2170563