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

摘要

We study the bifurcation curves of positive solutions of the boundary value problem{u"(x)f_ε(u(x))=0,_10.Thus the exact number of positive solutions can be precisely determined by the values ofand ε~*. We give an application to the two-parameter bifurcation problem {U"(x)+λ(1+u~2_εu~3)=O. _1