On solutions of some singular, nonlinear differential equations arising in boundary layer theory
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.
scientific article; zbMATH DE number 4204977
scientific article