The existence and blow-up rate of large solutions of one-dimensional pp-Laplacian equations

In this paper, we consider the existence, uniqueness and blow-up rate of positive solutions of the singular boundary value problem {(|u′(t)|p−2u′(t))′=f(t)h(u(t)),t>0,u(0)=+∞,u(+∞)=0, where ff is a nondecreasing and continuous function such that f(0)≥0f(0)≥0, and hh is a non-negative function satisfying the Keller–Osserman condition. Our results extend some previous findings of [S. Cano-Casanova, J. López-Gómez, Existence, uniqueness and blow-up rate of large solutions for a canonical class of one-dimensional problems on the half-line, J. Differential Equations 244 (2008) 3180–3203] in a certain sense.