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Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
Published online by Cambridge University Press: 20 November 2018
Abstract
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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).
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- Research Article
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- Copyright © Canadian Mathematical Society 1997
References
1.
Berestycki, H. and Lions, P.L., Nonlinear scalar field equations, I, Existence of a ground state, Arch. Rational Mech. Analysis
82(1983), 313–345.Google Scholar
2.
Faierman, M., Two-parameter eigenvalue problems in ordinary differential equations, Longman House, Essex, UK.Google Scholar
3.
Gidas, B.,Ni, W.M. and L.Nirenberg, Symmetry and related properties via the maximum principle, Commn. Math. Phys.
68(1979), 209–243.Google Scholar
4.
Shibata, T., Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems, J. Analyse Math.
66(1995), 277–294.Google Scholar
5.
Shibata, T., Variational eigencurve and bifurcation for two-parameter nonlinear Sturm-Liouville equations, Topol. Methods Nonlinear Anal.
8(1996. 79–93.Google Scholar
6.
Turyn, L., Sturm-Liouville problems with several parameters, J. Differential Equations
38(1980), 239–259.Google Scholar
7.
Zeidler, E., Ljusternik-Schnirelman theory on general level sets, Math. Nachr.
129(1986), 235–259.Google Scholar
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