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″-ρ2u+λa(t)f(u)=0,0 0 is a constant, a ∈ C([0, 1], [0, ∞)) with a(t0) > 0 for some t0 ∈ [0, 2π], f ∈ C([0, ∞), [0, ∞)) and f(s) > 0 for s > 0, and f0 = ∞, where f0=lims→0+f(s)/sf0=lims→0+f(s)/s. We investigate the global structure of positive solutions by using the Rabinowitz’s global bifurcation theorem.