On solutions of some singular, nonlinear differential equations arising in boundary layer theory (Q805912)

The author considers the problem \[ g(x)g''(x)+h(x)=0,\quad k<x<1,\quad g'(k)=C,\quad g(1)=0 \] which is the Crocco variable formulation of a differential equation arising in boundary layer theory with suction/injection. The function h is continuous, positive, and \(\lim_{x\to \infty}h(x)/x>0\). The solution is obtained as the solution of the problem with the boundary condition \(g(1)=0\) replaced by the initial condition \(g(k)=\alpha\) for an appropriate value of \(\alpha\). The analyticity of the solution, and some estimates of the initial value \(\alpha\) and the maximum point of the solution are also established.