Boundary value problems of nonsingular type on the semi-infinite interval
For the equation \[ y''+ \varphi(t) f(t,y,y')= 0,\quad 0<t<\infty, \] sufficient conditions are obtained for the existence of solutions that vanish at \(t=0\), are positive for \(t>0\), and satisfy one of the following three conditions: \(y\) is bounded on \([0,\infty)\), \(\lim_{t\to\infty} y(t)\) exists, and \(\lim_{t\to\infty} y'(t)= 0\). The proof is based on studying properties of the corresponding problems on the intervals \([0,n]\), \(n= 1,2,\dots\)\ .
scientific article; zbMATH DE number 1389726