Global structure of positive solutions for superlinear second-order periodic boundary value problems

We consider periodic boundary value problems of nonlinear second order ordinary differential equations of the form. u '' - rho(2)u + lambda a(t)f(u) = 0, 0 < t < 2 pi, u(0) = u(2 pi), u'(0) = u'(2 pi), where rho > 0 is a constant, a is an element of C([0,1], [0,infinity)) with a(t(0)) > 0 for some t(0) is an element of [0,2 pi], f subset 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 the Rabinowitz's global bifurcation theorem. (C) 2011 Elsevier Inc. All rights reserved.