Spectral asymptotics and bifurcation for nonlinear multiparameter elliptic eigenvalue problems
Tetsutaro Shibata · Bulletin of the Belgian Mathematical Society - Simon Stevin · 1996
This paper is concerned with the nonlinear multiparameter elliptic eigenvalue problem u′′(r) + N − 1 r u′(r) + μu(r)− k ∑ i=1 λifi(u(r)) = 0, 0 0, 0 ≤ r 0 is a normalizing parameter of eigenfunction associated with μ(λ, α). To this end, we shall establish asymptotic formulas of μ(λ, α) as |λ| → ∞, 0. Received by the editors November 1995. Communicated by J. Laubin. 1991 Mathematics Subject Classification : 35P30.