Uniqueness of positive solutions for some nonlinear fourth-order equations

In this paper we study the uniqueness question of positive solutions of the two point boundary value problem: u((4))(t) = f(u(t)), -R < t < R, u(+/-R) = u'(+/-R) = 0, where R > 0 is fixed and f:[0,infinity) --> [0,infinity) is in C-1. A uniqueness result is proved when f satisfies 0 < f(u) < uf'(u) for u > 0. Some examples are also given. (C) 1996 Academic Press, Inc.