ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35J60, 35P30 Shibata, Tetsutaro, Hiroshima University, Japan Asymptotic behavior of eigenvalues of nonlinear elliptic twoparameter problems We consider nonlinear two-parameter problem −Δu+λg(u) = μf(u) in Ω ⊂ R^{N}(N ≥ 3), u = 0 on ∂Ω, where Ω is a bounded domain, and λ, μ > 0 are parameters. By variational methods, the variational eigenvalues μ = μ(λ) are defined. We establish asymptotic formulas for μ(λ) as λ → ∞.