The Angular Distribution Of Solutions Of Higher Order Linear Differential Equations

This paper, based on the Nevanlinna fundamental theory and Wiman-Valiron theory, investigates the radial oscillation of infinite order solutions of higher order linear differential equation. The whole paper can be divided into the following four chapters.Chapter one, as the pre-knowledge of the whole paper, briefly introduces the relevant knowledge of Nevanlinna theory.Chapter two mainly investigates the radial oscillation of infinite order solutions of higher order nonhomogeneous linear differential equation f+(k)+Ak-1f(k-1)+…A1f’=F.In the condition that A0,A1,…,Akk-1, F with finite order and the transcendental solutions f satisfy σ2(f)=ρ(0<ρ<∞),then we can obtained an equivalent relationship between the estimations on the hyper order along radial direction of f, the hyper order and the hyper order convergence exponent of the sequence of zero of f along it’s Borel direction of hyper order,by using Nevanlinna theory in angular domain.Chapter three suppose that the infinity order solution f of f+(k)+Ak-1f(k-1)+…A1f’=F satisfy σ2(f)<∞and F with finite order, p(z) is the infinity order type function of Xiong Qinglai’s of f.Then obtain a sufficient and necessary condition for L:arg z=θ is a order Borel direction of f by using the infinity order type function of Xiong Qinglai’s and a sufficient and necessary condition for infinity order Borel direction which was established by Chuang Chitai.Chapter four studies the growth of transcendental solutions of the second order linear differential equation f"+h(Z)ep(Z)f’+Q(z)f=0with meromorphic coefficients and estimates the order and hyper order of the by specifying appropriate prerequisites by using Nevanlinna theory, Wiman-waliron theory.