A Method for Studying Oscillations of Nonlinear Differential Equations. Applications to Some Equations in Biology and Economics

Abstract

In this paper we give a new method for studying oscillations of large classes of nonlinear ordinary differential equations involving the Riccati equation, the Schrödinger and the Painlevé type equations. Some application are given as well.

On a Nevanlinna type result for solutions of nonautonomous equations y′=a( t) F 1( x,y), x′=b( t)F 2( x,y )

“…, q, we obtain n ÃÃ ðt 1 , t 2 , a Þ þ X q ¼1 n ÃÃÃ ðt 1 , t 2 , a Þ ffiffi ffi 2 p AKðd Þ t 2 À t 1 j j so that Theorem 1.3 immediately follows from (2.9), (2.11) and the last inequality. Finally we mention, that another geometric method developed earlier for meromorphic functions [2] has also been used recently for studying solutions of differential equations [1].…”