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)ψ(t) to the singular boundary value problemu″(t)=b(t)g(u(t)),u(t)>0,t>0,u(0)=∞,u(∞)=0, where b∈C1(0,∞)b∈C1(0,∞), which is positive and non-decreasing on (0,∞)(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)≅upg(u)≅up (p>1p>1) for sufficiently large u.