On the Existence of Positive Solutions for Some Nonlinear Boundary Value Problems II

الأصل · EN

We study a class of boundary value problems with φ-Laplacian (e.g., the prescribed mean curvature equation, in which φ(s)=s√1+s²) center -(φ(u'))'=λf(u) on (-L, L), u(-L)=u(L)=0, center where λ and L are positive parameters. For convex f with f(0)=0, we establish various results on the exact number of positive solutions as well as global bifurcation diagrams. Some new bifurcation patterns are shown. This paper is a continuation of Pan and Xing [13], where the case f(0)>0 has been investigated.