Singular cases of the problem of continuation of the boundary-layer

Assume that the pessure gradient $p_x$ is positive and satisfies the following inequalities: $p_x\leqslant p_x(0)(1-c_1x)^\alpha$, $\alpha>-1$ or $p_x\leqslant p_x(0)(1+c_2x)^\beta$, $\beta<-1$; $c_1, c_2>0$. The conditions for the existence and the uniqueness of the continuation of the boundary layer near the solid wall are obtained.