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 (vertical bar u'vertical bar(p-2)u')' = f (u) in (0, 1), u(0) = infinity, u(1) = infinity where p > 1 provided f is an element of C-1(0, infinity) boolean AND C-0 [0, infinity) with f (s) > 0 and f' (s) >= 0 for s is an element of (0, infinity). We see that the same result still holds for some equations with special nonlinearities satisfying f(s) > 0 and f'(s) >= 0 for s is an element of (0, infinity) in higher dimensions, but we conjecture that the same result should be true for equations with general nonlinearities satisfying f (s) > 0 and f' (s) >= 0 for s is an element of (0, infinity) in higher dimensions. (c) 2005 Elsevier Ltd. All rights reserved.