A nonselfadjoint dynamical system

Abstract

This paper concerns criteria for assuring that every solution of a real fourth order nonselfadjoint differential equationis oscillatory at x = ∞. Our technique is a generalisation of that used by Whyburn (1) for the study of the selfadjoint equation,combined with the theory of H-oscillation of vector equations as introduced by Domšlak (2) and studied by Noussair and Swanson (3). Whyburn's technique consists of representing (1.2) as a dynamical system of the formand then studying (1.3) in terms of polar coordinates in the y, z-plane. In Section 2 below we show how to represent (1.1) as a dynamical system of the form