共查询到20条相似文献,搜索用时 31 毫秒
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高凌云 《数学物理学报(B辑英文版)》2010,(5):1507-1513
In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the solutions, and obtain an interesting result, which extends Gaekstatter and Laine's result concerning complex differential equations to the systems of algebraic differential equations. 相似文献
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NECESSARYANDSUFFICIENTCONDITIONSFOREXISTENCEANDUNIQUENESSOFPERIODICSOLUTIONSOFNEUTRALLINEARFUNCTIONALDIFFERENTIALEQUATIONSWIT... 相似文献
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In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases. 相似文献
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On the Growth of Components of Meromorphic Solutions of Systems of Complex Differential Equations 总被引:3,自引:0,他引:3
Ling-yun Gao 《应用数学学报(英文版)》2005,21(3):499-504
This paper investigates the problem of the growth of the components of meromorphic solutions of a class of a system of complex algebraic differential equations, and generalized some of N. Toda's results concerning the growth of differential equations to the case of systems of differential equations. The paper considers the existence of admissible solutions of the system of differential equations. 相似文献
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This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form. 相似文献
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Sh. A. Makhmutov 《Differential Equations》2011,47(2):283-286
We estimate the growth of the spherical derivative for meromorphic solutions of algebraic differential equations of arbitrary
order under certain conditions on the growth of the coefficients. 相似文献
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Sébastien Boisgérault 《Comptes Rendus Mathematique》2013,351(15-16):645-648
This paper deals with delay-differential algebraic equations, a large class of linear and finite-memory functional differential equations. We introduce several representations of delay operators that provide a simple definition for the concept of solutions of such systems. Then we study exponential solutions and prove that the rightmost zeros of a system characteristic function determine its growth bound. 相似文献
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高凌云 《数学物理学报(B辑英文版)》2011,31(2):541-548
Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results. 相似文献
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Applying the Nevanlinna theory of meromorphic function,we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result.Meanwhile,we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are non-admissible.Moreover,the form of the systems of equations with admissible solutions is discussed. 相似文献
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《数学物理学报(B辑英文版)》2016,(3)
The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coefficients.Several theorems on the existence of solutions are obtained,which perfect the solution theory of linear complex differential equations. 相似文献
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Ulrich Staude 《manuscripta mathematica》1971,5(3):251-274
Strongly elliptic systems of nonlinear partial differential equations are considered in the case when the derivatives of the solutions occuring in the nonlinear terms have the same order as those in the linear principal part. The existence of periodic solutions for such systems is investigated. It is shown that this problem can be reduced to the study of algebraic bifurcation equations, whose small solutions correspond to the classical solutions of the given problem. A discussion of the bifurcation equations will be given in a forthcoming paper. 相似文献
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In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the solutions, and obtain an interesting result, which extends Gackstatter and Laine's result concerning complex differential equations to the systems of algebraic differential equations. 相似文献
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Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations. 相似文献
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本文研究了高阶复线性微分方程解在角域上的增长性问题.利用Nevanlinna理论和共形变换的方法,获得了一些使得方程非平凡解在角域上有快速增长的系数条件,这些结果丰富了复方程解在角域上增长性的研究. 相似文献
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Systems of linear partial differential equations with constant coefficients are considered. The spaces of formal and analytic solutions of such systems are described by algebraic methods. The Hilbert and Hilbert—Samuel polynomials for systems of partial differential equations are defined. 相似文献
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V. A. Gorelov 《Mathematical Notes》2013,94(1-2):82-95
We consider hypergeometric functions satisfying homogeneous linear differential equations of arbitrary order. We prove general theorems on the algebraic independence of the solutions of a set of hypergeometric equations as well as of the values of these solutions at algebraic points. The conditions of most theorems are necessary and sufficient. 相似文献