The number of bifurcation points of a periodic one-parameter ODE with at most two periodic solutions Original Research Article

We study the number of bifurcation points of x′=F(t,x,λ), where F is periodic in t, continuous, and locally Lipschitz continuous with respect to x, by assuming that the differential equation has at most two periodic solutions for each View the MathML source. Under some additional assumptions we prove that there are at most two bifurcation points and we find sufficient conditions under which this equation has exactly k bifurcation values, where k=0,1,2.