Singular nonlinear differential equations on the half line (Q1381011)

The paper presents existence results for boundary value problems on the half line of the form \[ -y'' = q(t)f(t,y,y') \quad\text{for}\quad 0<t<\infty, \] \(y(0)=0\), \(y\) bounded on \([0,\infty )\), where \(f\) may be singular at \(y=0\). The discussion follows three steps. First, it is considered the corresponding problem on a finite interval \([0,n]\), \(n \in N^*\) with boundary conditions \(y(0)=0\) and \(y(n)=b>0\). Secondly, the Ascoli-Arzela theorem and a diagonalization argument yield a global solution. Finally, the boundary condition at infinity is discussed. The main tool is the Leray-Schauder continuation principle. Some other boundary conditions at infinity are also examined.