Article contents
Spectral properties of a two parameter nonlinear Sturm-Liouville problem
Published online by Cambridge University Press: 14 November 2011
Synopsis
We consider the nonlinear Sturm–Liouville problem with two parameters on the general level set
We establish asymptotic formulae of the n-th variational eigenvalue λ = λn(μ, α) as α→∞ and α↓(nπ)2.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 6 , 1993 , pp. 1041 - 1058
- Copyright
- Copyright © Royal Society of Edinburgh 1993
References
1Beresticki, H.. Le nombre de solutions de certain problerhes semi-lineaires elliptiques. J. Fund. Anal. 40 (1981), 1–29.CrossRefGoogle Scholar
2Binding, P. and Browne, P. J.. Asymptotics of eigencurves for second order ordinary diff9rential equations, I. J. Differential Equations 88 (1990), 30–45.CrossRefGoogle Scholar
3Crandall, M. G. and Rabinowitz, P. H.. Bifurcation from simple eigenvalues. J. Funct Anal. 8 (1971), 321–340.CrossRefGoogle Scholar
4Itô, K. (ed.). Encyclopedic Dictionary of Mathematics, 2nd edn, Vol. 4 (Cambridge Massachusetts: MIT Press, 1987).Google Scholar
5Shibata, T.. Nodal and asymptotic properties of solutions to nonlinear elliptic eigenvalue problems on general level sets. Israel J. Math. 74 (1991), 225–240.CrossRefGoogle Scholar
6Zeidler, E., Ljusternik-Schnirelman theory on general level sets. Math. Nachr. 129 (1986), 235–259.CrossRefGoogle Scholar
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