Remarks on uniqueness of boundary blow-up solutions

We show that there is at most one nonnegative boundary blow-up solution for the one-dimensional boundary blow-up problem (|u′|p−2u′)′=f(u)in (0,1),u(0)=∞,u(1)=∞ where p>1p>1 provided f∈C1(0,∞)∩C0[0,∞)f∈C1(0,∞)∩C0[0,∞) with f(s)>0f(s)>0 and f′(s)≥0f′(s)≥0 for s∈(0,∞)s∈(0,∞). We see that the same result still holds for some equations with special nonlinearities satisfying f(s)>0f(s)>0 and f′(s)≥0f′(s)≥0 for s∈(0,∞)s∈(0,∞) in higher dimensions, but we conjecture that the same result should be true for equations with general nonlinearities satisfying f(s)>0f(s)>0 and f′(s)≥0f′(s)≥0 for s∈(0,∞)s∈(0,∞) in higher dimensions.