Blow-up rate of the unique solution for a class of one-dimensional problems on the half-line
The authors show the exact blow-up rate of the unique positive solution \(\psi\) to the singular boundary value problem \[ \begin{cases} u''(t)=b(t)g(u(t)), t>0,\\ u(0)=\infty,\quad u(\infty)=0, \end{cases} \] where \(b\in C^1(0,\infty)\) is positive and non-decreasing, and \(g\in C^1[0,\infty)\) is increasing and satisfies \(g(0)=g'(0)=0\), \(\int_0^1{\frac{d\nu}{ g(\nu)}}=\infty\), and \(\lim_{s\to\infty}{\frac{sg'(s)}{g(s)}}=p>1\). As the authors explain, the main result is inspired by the paper of \textit{S. Cano-Casanova} and \textit{J. López-Gómez} [J. Differ. Equations 244, No. 12, 3180--3203 (2008; Zbl 1149.34020)].
scientific article; zbMATH DE number 5355976