ABSTRACT
Oscillation of systems of neutral differential equations is an interesting and hard problem. This chapter employs the definition for weaker oscillation. It presents some explicit conditions for oscillation of system using Lozenskii measures, or logarithmic norms, of matrices. The criteria are sharp in the sense that even for the scalar case they are still the best known. Oscillation criteria are obtained by comparing the system with some systems with constant matrix coefficients. The chapter describes the nonautonomous system. It obtains some comparison results for oscillation of systems with scalar equations. The chapter also presents some results on the existence of nonoscillatory solutions. It derives oscillation properties for Lotka-Volterra models in the system cases. The chapter considers the existence of nonoscillatory solutions of nonlinear systems of neutral differential equations. It determines conditions for the system to possess nonoscillatory solutions with the asymptotic behavior limit.
