We consider the nonlinear eigenvalue problem
[D(u(t))u(t)']' + λg(u(t)) = 0,
u(t) > 0 ; t ∈ I := (0, 1), u(0) = u(1) = 0,
which comes from the porous media type equation. Here, D(u) = pu2n+sin u (n ∈ N, p > 0: given constants), g(u) = u or g(u) = u + sin u. λ > 0 is a bifurcation parameter which is a continuous function of α = ||uλ||∞ of the solution uλ corresponding to λ, and is expressed as λ = λ(α). Since our equation contains oscillatory term in diffusion term, it seems significant to study how this oscillatory term gives effect to the structure of bifurcation curves λ(α). We propose a question from a view point of inverse bifurcation problems and show that the simplest case D(u) = u2 + sin u and g(u) = u gives us the most impressible asymptotic formula for global behavior of λ(α).
