ABSTRACT
Oscillation and nonoscillation of systems of nonlinear differential equations is an interesting problem. In this chapter we will present some recent contributions.
In Sections 7.2 and 7.3, we consider oscillation of all solutions of systems of nonlinear differential equations with or without forcing. Some oscillation criteria are presented. In Sections 7.4 and 7.5, we classify positive solutions of our systems according to their limiting behaviors and then provide necessary and sufficient conditions for their existence. Then, in Section 7.6, we provide a classification scheme for positive solutions of two-dimensional second order differential systems and give conditions for the existence of solutions with designated asymptotic properties. Section 7.7 is concerned with nonoscillation of systems of differential equations of the Emden-Fowler type. Several necessary and/or sufficient conditions for strong nonoscillation are given. Here we use the definitions for strong oscillation and strong nonoscillation given in Chapter 1, i.e., a vector solution is said to be strongly oscillatory (strongly nonoscillatory) if each of its nontrivial components has arbitrarily large zeros (is nonoscillatory).
