A note on \(f'''+ff''+\lambda(1-{f'}^2)=0\) with \(\lambda\in(-\frac{1}{2},0)\) arising in boundary layer theory. (Q1767220)

The author gives an existence results in the space \(C^{1}[0,+\infty [ \) of the following problem \[ f^{\prime \prime \prime }+ff^{\prime \prime }+\lambda (1-(f^{\prime }) ^{2}) =0 \text{ a.e. on }[0,+\infty [,\quad f(0) =f^{\prime }(0) =0, \;\;f^{\prime }(+\infty ) =1, \] with \( \lambda \in (-\frac{1}{2},0) .\) This problem arises in boundary layer theory in fluid mechanics. For the proof, he uses the Schauder fixed-point theorem.