The Growth Of Solutions Of (Systems Of ) Algebric Differential Equations

In this thesis, by means of the Nevanlinna theory of meromorphic functions andnormal family theory, we investigate the growth of solutions of the algebric differentialequationa(z)w 2 + (b2(z)w2 + b1(z)w + b0(z))w = d3(z)w3 + d2(z)w2 + d1(z)w + d0(z),and the growth of solutions of systems of the algebric differential equation(w2)m1 = a(z)w1(n ),(w1(n ))m2 = ?(w2).The first chapter introduces the thesis'studying work, studying purpose, back-ground and so on. The second chapter outlines the basic knowledge of Nevanlinnatheory of meromorphic functions and normal family theory. In the third chapter, weconsider the growth of solutions of some algebric differential equations, two goodconclusions are geted. One is to push the conclusion of Yuan, Xiao and Zhang[25]to the case of entire solutions, and the upper bound is even smaller. Another is touse the conclusion of Liao and Yang[21] to get a special class of first-order algebraicdifferential equation, in which the order of any transcendental entire solution is one.In the forth chapter, we give an estimation of the growth order of solution of a typeof systems of algebric differential equations by using Zalcman Lemma and methodof Wenjun Yuan and other authors, and extend the result of Xianfeng Su[17]. Someto-be-solved problems are given out in the fifth chapter.