Blow-up rate of the unique solution for a class of one-dimensional \(p\)-Laplacian equations
The exact blow-up rate of the unique solution of the singular boundary value problem \[ \begin{aligned} (|u'|^{p-2}u')'=b(t)f(u),\;u(t)>0,& \quad t>0, \\ u(0)=\infty, \quad u(\infty)=0,& \end{aligned} \] is obtained, where \(1<p \leq 2\), \(b \in C^1(0,\infty)\) is positive and nondecreasing on \((0,\infty)\), \(f \in C^1[0,\infty)\), \(f(0)=0\), \(f(u)/u\) is increasing on \((0,\infty)\).
scientific article; zbMATH DE number 6118814