Non-linear multiparameter eigenvalue problems for ordinary differential equations

AbstractIn this paper we consider the non-linear multiparameter eigenvalue problem in ordinary differential equations: y″r(xr) + qr(xr)yr(xr) + Mr(yr) + ∑s = 1n μs(ars(xr + Prs) yr(xr) = 0, r = 1,…, n, where the non-linear functions Mrand Prs will be required to satisfy certain Fréchet differentiability conditions. We study bifurcation from the simple eigenvalues of the corresponding linear problem and state a completeness theorem for the eigenfunctions of these systems