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 = λ 1 , 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 = λ 1 on this curve. Similarly, we consider oscillatory bifurcation from zero.