On a codimension 3 bifurcation of plane vector fields with symmetry
We discuss an open question of Kiguradze and Chanturia about Property and Property for the equation . The proposed integral criterion is proved in a few cases.
The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].
In this paper we will study some asymptotic properties of a nonlinear third order differential equation viewed as a perturbation of a simpler nonlinear equation investigated recently by the authors in [4].