#### Xuemei Zhang, Meiqiang Feng, Exact number of positive solutions for classes of multi-parameter quasilinear equations, 2016 (2016), Article ID 25 (23 May 2016)

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Abstract

Using a detailed analysis of time maps, the exact number of positive solutions is obtained for the quasilinear prescribed mean curvature equation $-\bigg(\frac{u'}{\sqrt{1+u'^2}}\bigg)'=\lambda (u^p-u^q),$ $u(x)>0,$ $-L< x< L,$ $u(-L)=u(L)=0,$ where $\lambda>0$ is a bifurcation parameter, $L>0$, the radius of the one-dimensional ball $(-L,L)$, is an evolution parameter, and p, q with $-1 and $p\neq q$ are two constants. The precise bifurcation diagrams are also given.