The existence and blow-up rate of large solutions of one-dimensional \(p\)-Laplacian equations (Q420097)

Existence, uniqueness and blow-up rate of positive solutions of the singular boundary value problem NEWLINE\[NEWLINE \left\{\begin{aligned} &(|u'|^{p-2}u')' = f(t)h(u), \quad t>0, \\ &u(0)=+\infty, \quad u(+\infty) = 0 \end{aligned}\right. NEWLINE\]NEWLINE are studied, where \(1<p\leq 2\), \(f\in C[0,\infty)\) is nondecreasing, \(f(t)>0\) for \(t>0\), \(h \in C^1[0,\infty)\), \(h(0)=0\), \(h'(u)>0\) for \(u>0\), and NEWLINE\[NEWLINE \int_t^\infty \left( \int_t^s h(\tau) d\tau \right)^{-1/p}\, ds < +\infty, \quad t>0. NEWLINE\]