The Growth And Borel Directions Of Solutions Of Higher Order Differential Equations

In this thesis,we investigate some properties of the higher order linear differentialequations by using Nevanlinna’s value distribution theory and methods. The propert-ies mainly contain the growth of solutions of the differential equations, the borel dire-ction and the argument distribution. The thesis is divided into four chapters.In chapter1, we introduced the research background of linear differential equati-ons.Then we narrate some notations and knowledge which will be used in the followi-ng chapters.In chapter2, we investigate the growth of solutions of the differential equationf (k) A fk1k1Af0and corresponding non-homogeneous differential equat-ion．Assume someAs (1s k1)is entire functions with a finite deficient value,we proved that every solution f0of the homogeneous differential equation has infi-nte order and the same condition as non-homogeneous except for an extra solution.In chapter3, we proved that the meromorphic function f (z)and g(z)1f23f4have the consistent Borel direction,where1,2,3,4are the small fuctions of f(z)Then by using the above results we obtain that the solutions to a class of higher orderlinear homogeneous differential equations have the consisten Borel direction.In chapter4, we study the relation between zero accumulation line and the Boreldirection ofE f1fk,wheref1,,fkare the linearly independent solutions ofsome differential equation，and further consider that the infinite hyper order and theinfinite hyper zero exponent of convergence ofEin the angle domain are equivalent...