CAJ | 학술논문

利用Nevanlinna的值分布理论和分类讨论的思想方法，研究了一类高阶齐次线性微分方程f（k）＋Hk－1f（k－1）＋?＋H1f′＋H0f＝0解的增长性，得到了一些有意义的结果：当Hj（z）（j＝0，1，?，k－1）是整函数时，根据线性微分方程的一般理论，上述方程的每个解都是整函数．当方程系数满足：Hj（z）＝hj（z）ePj（z）（j＝0，1，?，k－1）， Pj（z）是首项系数为aj的n （n≥1）次多项式， hj（z）为整函数，σ（hj（z））＜n， aj 是复数，存在as 和al，使得l＞s， as ＝dseiφ， al ＝－dleiφ， ds ＞0， dl ＞0．对j≠s，l， aj＝djeiφ（dj≥0）或aj ＝－djeiφ， max｛dj；j≠s，l｝＝d＜min｛ds， dl｝， hshl厨0，给出了该微分方程的每个超越解的超级的精确估计．结果可以推广到亚纯函数系数的微分方程．
이용Nevanlinna적치분포이론화분류토론적사상방법，연구료일류고계제차선성미분방정f（k）＋Hk－1f（k－1）＋?＋H1f′＋H0f＝0해적증장성，득도료일사유의의적결과：당Hj（z）（j＝0，1，?，k－1）시정함수시，근거선성미분방정적일반이론，상술방정적매개해도시정함수．당방정계수만족：Hj（z）＝hj（z）ePj（z）（j＝0，1，?，k－1）， Pj（z）시수항계수위aj적n （n≥1）차다항식， hj（z）위정함수，σ（hj（z））＜n， aj 시복수，존재as 화al，사득l＞s， as ＝dseiφ， al ＝－dleiφ， ds ＞0， dl ＞0．대j≠s，l， aj＝djeiφ（dj≥0）혹aj ＝－djeiφ， max｛dj；j≠s，l｝＝d＜min｛ds， dl｝， hshl주0，급출료해미분방정적매개초월해적초급적정학고계．결과가이추엄도아순함수계수적미분방정．
By utilizing Nevanlinna's value distribution theory of meromorphic functions and categorized discussion method, the growth of solutions of higher order differential equations is investigated and some important results are obtained.When Hj(z) (j=0,1,?,k-1) are entire functions, according to the general theory of linear differential equations, every solution of the above equations with entire coefficients is entire function.When the coefficients of the above equations satisfy:Hj(z)=hj(z)ePj(z) (j=0,1,?,k-1),Pj(z) are polynomials with degree n and lead-ing coefficients aj, hj(z) are entire functions,σ(hj(z))<n, aj are complex number, l>s, as=dseiφ, al=-dleiφ, ds>0, dl >0.For j≠s,l, aj=djeiφ(dj≥0) or aj=-djeiφ, max{dj;j≠s,l} =d<min{ds, dl}, hshl0, and the precise estimation of the hyper-order of their transcendental solutions of the class of linear differential equations is given.The results obtained in this paper can be extended to differential equations with meromorphic coefficients.