A modified Picone-type identity and the uniqueness of positive symmetric solutions for a prescribed mean curvature problem

In this article, we study the uniqueness of positive symmetric solutions of the following mean curvature problem in Euclidean space: {{u'/root 1+divided by u'divided by(2)}(') +h(x)f(u) = 0, -1 < x < 1, {u(-1) = u(1) = 0,where h is an element of C-1([-1,1]) and f is an element of C-1([0, infinity); [0, infinity)). Under suitable conditions on h and monotone condition on f(s)/s, by introducing a modified Picone-type identity, we prove that the problem has at most one positive symmetric solution.