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Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity

Published online by Cambridge University Press:  20 November 2018

Tetsutaro Shibata
Tetsutaro Shibata*
Affiliation:
The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739 Japan
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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).

Keywords

34B1534B25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 5 , 01 October 1997 , pp. 1066 - 1088
Copyright
Copyright © Canadian Mathematical Society 1997

References

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