Three positive nonconstant radial solutions of nonlinear Neumann problems with indefinite weight

In this article, we consider the global behavior of components of positive nonconstant radial solutions for the Neumann problem with indefinite weight {-Delta u = lambda h(X)f(u), in B, partial derivative(nu)u = 0, on partial derivative B, where lambda > 0 is a parameter, B subset of R-N(N >= 1) is the unit open ball, f is an element of C([0, infinity), [0, infinity)) and h is an element of C((B) over bar) satisfying integral(B) h(x) dx < 0 is the sign-changing function. We determine the intervals of lambda in which the above problem has one, two or three positive nonconstant radial solutions by using the directions of a bifurcation.