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Growth of Solutions of Higher Order Complex Linear Differential Equations in an Angular Domain of Unit Disc 下载免费PDF全文
Jianren Long 《数学研究》2015,48(3):306-314
We study the growth of solutions of higher order complex differential equations
in an angular domain of the unit disc instead of the whole unit disc. Some conditions
on coefficient functions, which will guarantee all non-trivial solutions of the
higher order differential equations have fast growing, are found in this paper. 相似文献
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Feng Chun 《Annals of Differential Equations》2005,21(3):268-270
In this paper, we study the growth of the solutions for 1st kind of differential equations of higher order in the unit disc. We give a sufficient condition for all solutions of second order linear differential equation to be inadmissible and a sufficient condition for all solutions of higher order linear differential equation to be of infinite order. 相似文献
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Zong-Xuan Chen 《Journal of Mathematical Analysis and Applications》2004,297(1):285-304
In this paper, we classify the functions of small growth in the unit disc to different degree, and investigate the growth of solutions for certain linear differential equations with coefficients of small growth in the unit disc. 相似文献
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该文在方程系数A_0的增长性起支配作用的条件下,研究了一类高阶线性齐次微分方程解的增长性,得到两个主要结果,一个是全平面的,一个是单位圆的,改进和推广了原有的一些结果. 相似文献
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研究了有限迭代级整系数的复线性微分方程,应用Nevalinna和Ahlfors的角域理论,得到了有关解的迭代级,零点迭代收敛指数以及角域中的零点分布的结果. 相似文献
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Cao Tingbin 《Annals of Differential Equations》2005,21(2):111-122
In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions. 相似文献
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结合微分方程理论和函数空间理论,研究了单位圆上一类特殊高阶线性微分方程解的性质,得到当方程系数满足某些条件时,其解属于某类函数空间的充分条件. 相似文献
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Klaus Böhmer 《manuscripta mathematica》1970,3(4):343-356
In this paper the solutions of the differential equation (D) wm + am–1 (Z) Wm–1. + ao(Z)=0 are discussed. In the definitions 1,2,3 functions are given measuring the growth of the coefficients resp. of the solutions of (D). Theorem 1 shows, that the l-fold iterated order of growth of the coefficients equals to the (l+1)-fold iterated order of growth of the solutions. In the case l==o theorem 1 passes over to the well known FUCHSian theory of regular singular points. Using proximate order theorem 4 gives an improved version of theorem 1.
Herrn Professor Dr.R.Nevanlinna zum 75. Geburtstag gewidmet 相似文献
Herrn Professor Dr.R.Nevanlinna zum 75. Geburtstag gewidmet 相似文献
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讨论了系数是单位圆内解析函数的二阶齐次和非齐次线性微分方程的解及其一阶导数和二阶导数与小函数之间的关系,并得到了它们之间的精确估计. 相似文献
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该文将几个全纯函数空间的定义从单复变数推广到多复变数, 这些空间中全纯函数的增长性依赖于某个权函数. 作者研究了它们的增长性与边界值的关系以及这些空间相互之间的对偶关系, 所用方法和技巧与单复变数有不少区别. 所得到的结论是单复变数许多已知结果的推广. 相似文献
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开口弧段Γ上的双解析函数的Riemann边值问题与单位圆周L上双解析函数的Hilbert边值问题复合而成的一般复合边值问题,当L与Γ发生微小的光滑摄动后,借助于推广的拉甫伦捷夫近似于圆的共形映射,将星形域映为单位圆域,从而得出摄动后的问题的解的表达式,同时讨论了解的稳定性情况,并给出误差估计. 相似文献
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Nan Wu 《Results in Mathematics》2014,65(1-2):57-66
In this paper, we consider the growth order of solutions of higher order linear differential equations in a sector of the unit disk instead of the whole unit disk. 相似文献
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In this paper we investigate the iterated order, iterated type and iterated convergence exponent of zeros of meromorphic solutions of the equations
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Christer Glader Mikael Lindström 《Journal of Mathematical Analysis and Applications》2002,273(2):417-427
We show how to construct all finite Blaschke product solutions and the minimal scaled Blaschke product solution to the Nevanlinna-Pick interpolation problem in the open unit disc by solving eigenvalue problems of the interpolation data. Based on a result of Jones and Ruscheweyh we note that there always exists a finite Blaschke product of degree at most n−1 that maps n distinct points in the closed unit disc, of which at least one is on the unit circle, into n arbitrary points in the closed unit disc, provided that the points inside the unit circle form a positive semi-definite Pick matrix of full rank. Finally, we discuss a numerical limiting procedure. 相似文献
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Evgueni Doubtsov 《Archiv der Mathematik》2014,102(4):391-399
We show that N.G. Makarov’s law of the iterated logarithm governs the radial growth of weighted Bloch functions in the complex unit ball. The argument is based on an analog of M. Weiss’ theorem for special lacunary series in the ball. 相似文献
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J A Bennell C N Potts J D Whitehead 《The Journal of the Operational Research Society》2002,53(10):1109-1117
In the min-max loop layout problem, machines are to be arranged around a loop of conveyor belt. The ordering of the machines dictates the number of circuits of the conveyor belt required to manufacture each of several products. The goal is to find an ordering of the machines that minimises the maximum number of circuits required for the manufacture of any of the products. Since the problem is strongly NP-hard, the study of heuristic methods is of interest. This paper proposes iterated descent and tabu search algorithms, and a randomised insertion algorithm. Results of extensive computational tests show that all of our algorithms outperform a previously known algorithm that applies a greedy heuristic to the solution of a linear programming relaxation. The best quality solutions are obtained with iterated descent. This adds further evidence to the belief that iterated descent can produce high quality solutions to a variety of combinatorial optimisation problems. Moreover, unlike some other local search algorithms, iterated descent does not require much tuning in order to be competitive. 相似文献
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The concept of logarithmic order in the unit disc forms a bridge between meromorphic functions of unbounded Nevanlinna characteristic and meromorphic functions of (usual) zero order of growth. A collection of fundamental results for meromorphic functions of finite logarithmic order is given. Some of these results are reminiscent from the finite order case. Part I of this paper culminates in solving the inverse problem related to the famous defect relation in the case of finite logarithmic order. Part II deals with the analytic case. 相似文献