On Bendixson′s Criterion

AbstractFor autonomous differential equations in Rn criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories. The technique is based on the study of functionals on 2-surfaces. Results generalize to higher dimensions a criterion of Bendixson for the nonexistence of nonconstant periodic solutions in the case n = 2. As an example, an application to the Lorenz system in R3 is given