An application of maximum principle with respect to quenching problems

In this article, we use the maximum principle of Protter and Weinberger [1] (see also [2]) to confirm the uniqueness of a positive global solution of w′ʹ − 12yw′ = ƒ(w(y)): = w−β (y) − w(y)β + 1 in (0, ∞); w′(0) = 0, (IBVP) wβ(y)w′ʹ(y) = 1 + wβ(y) (12yw′(y) − w(y)β + 1) ≤ 1 in (0, ∞) is the constant solution w(y) = κ: = (β + 1)1(β + 1), where β > 0 is a given constant.