GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR SUPERLINEAR 2mth-BOUNDARY VALUE PROBLEMS

We consider boundary value problems for nonlinear 2mth-order eigenvalue problem (-1)(m)(u)(2m)(t) = lambda alpha(t)f(u(t)), 0<t<1, u((2i))(0) = u((2i))(1) = 0, i=0,1,2,..., m-1. where a is an element of C([0, 1], [0, infinity)) and a(t(0)) > 0 for some t(0) is an element of [0, 1], f is an element of C([0, infinity), [0, infinity)) and f(s) > 0 for s > 0, and f(0) = infinity, where f(0) = lim (s -> 0+) f(s)/s. We investigate the global structure of positive solutions by using Rabinowitz's global bifurcation theorem.