Multiparameter Variational Eigenvalue Problems With Indefinite Nonlinearity
Tetsutaro Shibata · Canadian Journal of Mathematics · 1997
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).