On the existence of steady flow in a channel with one porous wall or two accelerating walls

channel either with no-slip at one wall and constant uniform suction or injection through another wall, or with two accelerating walls. The flows are governed by the fourth order nonlinear differential equation $F^{iv}+R(FF'''-F'F'')=0$. In the former case, the flow is subject to the boundary conditions $F(-1)=F'(-1)=F'(1)=0$, $F(1)=-1$. In the latter case, the boundary conditions are $F(-1)=F(1)=0$, $F'(-1)=-1$, $F'(1) = 1$.