A theorem on reversed S-shaped bifurcation curves for a class of boundary value problems and its application

We study the bifurcation curves of positive solutions of the boundary value problem {u″(x)+fε(u(x))=0,−10ε∗>0. Thus the exact number of positive solutions can be precisely determined by the values of ε̃ and ε∗ε∗. We give an application to the two-parameter bifurcation problem {u″(x)+λ(1+u2−εu3)=0,−1