An oscillatory bifurcation from infinity, and from zero

The problem (where B is a unit ball in R ⁿ ) , with , is known to have a curve of positive solutions bifurcating from infinity at λ = λ₁, the principal eigenvalue. It turns out that a similar situation may occur, when g(u) is oscillatory for large u, instead of being small. In case n = 1, we can also prove existence of infinitely many solutions at λ = λ₁ on this curve. Similarly, we consider oscillatory bifurcation from zero.