Article contents
Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
Published online by Cambridge University Press: 20 November 2018
Abstract
We consider the multiparameter nonlinear Sturm-Liouville problem
where are parameters. We assume that
1 ≤ q ≤ p1 < p2 < ... ≤ pn < 2q + 3.
We shall establish an asymptotic formula of variational eigenvalue λ = λ(μ, α) obtained by using Ljusternik-Schnirelman theory on general level set Nμ, α(α < 0 : parameter of level set). Furthermore,we shall give the optimal condition of {(μ, α)}, under which μi(m + 1 ≤ i ≤ n : fixed) dominates the asymptotic behavior of λ(μ, α).
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1997
References
- 2
- Cited by