Blow-up rate of the unique solution for a class of one-dimensional problems on the half-line ✩

For more general nonlinear term g, the paper shows the exact blow-up rate of the unique solution ψ(t) to the singular boundary value problem u (t) = b(t)g(u(t)), u(t) > 0, t > 0, u(0)=∞, u(∞) = 0, where b ∈ C1(0,∞), which is positive and non-decreasing on (0,∞) (may vanish at zero). Our results are obtained in a more general setting to those in [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 (12) (2008) 3180– 3203], where g(u)∼= up (p > 1) for sufficiently large u