For the $p$-Laplace Dirichlet problem (where $\phi (t)=t|t{|}^{p-2}$, $p>1$)

$$\phi (u^{\prime }(x){)}^{\prime }+f(u(x))=0\mathrm{f}\mathrm{o}\mathrm{r}-1<x<1,u(-1)=u(1)=0$$

assume that $f^{\prime }(u)>(p-1)\frac{f(u)}{u}>0$ for $u>\gamma >0$, while ${\int }_u^{\gamma }f(t)dt<0$ for all $u\in (0,\gamma )$. Then any positive solution, with $\underset{(-1,1)}{max}u(x)=u(0)>\gamma$, is non-singular, no matter how many times $f(u)$ changes sign on $(0,\gamma )$. The uniqueness of solution follows.