# BVP: show existence and monotonicity

Consider the boundary value problem $$\begin{cases}y''+cy'+f(y)=0, & -M

where $$f$$ is some Lipschnitz non-linearity with $$f(0)=f(1)=0$$.

Use the sub- and super-solution approach to prove that for each pair (M,c) there exists a solution and that this solution is monotonous.

I think the existence is a direct consequence of the fact that $$u=0$$ is a subsolution and $$v=1$$ is a supersolution.

But what about the monotonicity of the existing solution? Is this a consequence of the strong maximum principle?