  We study a class of boundary value problems with $\varphi$-Laplacian (e.g.,
the prescribed mean curvature equation, in which
$\varphi(s)=\frac{s}{\sqrt{1+s^2}}$) \begin{center}
$-\left(\varphi(u')\right)'=\lambda f(u)\; \text{ on }(-L, L),\quad
u(-L)=u(L)=0,$ \end{center} where $\lambda$ 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.
