Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems

The nonlinear two-parameter Sturm-Liouville problem u '' + mu g(u) = lambda f(u) is studied for mu, lambda > 0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show the existence of an n-th variational eigenvalue lambda = lambda(n)(mu). Furthermore, for special f and g, the asymptotic formula of lambda(1)(mu) as mu --> infinity is established.