A class of nonlinear boundary value problems on the half line (Q1334709)

The paper deals with the problem (1) \(\varphi'' = f(\varphi)\), \(\varphi (0) = c(>0)\), \(\varphi (\infty) = 0\), where \(f\) is a function taken from certain model problems in the theory of colloids, the theory of plasmas or the theory of semiconductor devices. For example \(f(\varphi) = 2 \sin h \varphi\). Using the Leray-Schauder principle, the authors prove the existence and uniqueness of a positive solution \(\varphi\) of the above equations on the finite interval \([0,N)\) with \(\varphi (N) = 0\). Then, by a monotone limitting process \((N \to \infty)\), they get a solution of (1). Qualitative properties of the solution and constructive methods for finding it are presented here as well.