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研究了亚纯函数系数的二阶线性微分方程解的不动点及超级问题,得到了有关复域微分方程亚纯解的不动点性质,并且由于受到微分方程的制约,其性质与一般亚纯函数的不动点性质相比,显得十分有趣. 相似文献
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二阶线性微分方程亚纯解的不动点与超级 总被引:3,自引:0,他引:3
本文研究了以亚纯函数为系数的二阶线性微分方程的解及其一阶和二阶导数的不动点及超级问题,得到:二阶线性微分方程亚纯解及其一阶和二阶导数的不动点性质,由于受到微分方程的限制,与一般亚纯函数的不动点性质相比是十分有趣的,事实上,它们与解的增长性密切相关。 相似文献
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研究了一类亚纯函数系数的高阶线性微分方程的解的不动点问题,应用值分布的理论和方法,得到了复域微分方程亚纯解的不动点性质. 相似文献
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孙桂荣 《纯粹数学与应用数学》2011,27(3):348-356
运用值分布理论研究了高阶慢增长系数线性微分方程的解及其导数的不动点问题.当存在某个系数对方程的解的性质起主要支配作用时,得到了方程解及其导数的不动点收敛指数的精确估计,推广了有关文献中的结论. 相似文献
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本文研究了以整函数为系数的二阶线性微分方程解的幂和解生成的微分多项式的不动点问题,得到:二阶线性微分方程解生成的微分多项式的不动点性质,由于受到微分方程的限制,与一般亚纯函数的不动点性质相比是十分有趣的.事实上,它们与解的增长性密切相关. 相似文献
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关于高阶线性微分方程亚纯解的增长率 总被引:32,自引:0,他引:32
本文研究了二种类型的高阶线性齐次亚纯函数系数微分方程的亚纯解的增长性,当存在某个系数对方程的解的性质起主要支配作用时,我们对方程的亚纯解的增长率得到了精确的估计。 相似文献
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利用辅助方程与函数变换相结合的方法,构造了Degasperis-Procesi(D-P)方程的无穷序列类孤子新解.首先,通过两种函数变换,把D-P方程化为常微分方程组.然后,利用常微分方程组的首次积分,把D-P方程的求解问题化为几种常微分方程的求解问题.最后,利用几种常微分方程的Bcklund变换等相关结论,构造了D-P方程的无穷序列类孤子新解.这里包括由Riemannθ函数、Jacobi椭圆函数、双曲函数、三角函数和有理函数组成的无穷序列光滑孤立子解、尖峰孤立子解和紧孤立子解. 相似文献
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通过几个实例给出解非预解形式线性微分方程的一般方法,并讨论了预解形式的线性微分方程与非预解形式的线性微分方程解集的差别. 相似文献
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Riccati-Bernoulli辅助常微分方程方法可以用来构造非线性偏微分方程的行波解.利用行波变换,将非线性偏微分方程化为非线性常微分方程, 再利用Riccati-Bernoulli方程将非线性常微分方程化为非线性代数方程组, 求解非线性代数方程组就能直接得到非线性偏微分方程的行波解.对Davey-Stewartson方程应用这种方法, 得到了该方程的精确行波解.同时也得到了该方程的一个Backlund变换.所得结果与首次积分法的结果作了比较.Riccati-Bernoulli辅助常微分方程方法是一种简单、有效地求解非线性偏微分方程精确解的方法. 相似文献
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M. M. Lavrent’ev V. I. Maksimov 《Computational Mathematics and Mathematical Physics》2008,48(4):641-647
A parabolic equation under the influence of external perturbations is considered. It is assumed that the solutions to this equation are measured (possibly with errors). The problem of construction of differential equations for estimation (reconstruction) of perturbations using the measured data is discussed. Differential equations of the auxiliary system whose right-hand sides are approximations of the unknown input are derived. 相似文献
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The paper contains various theorems on the propagation of the invariance of germs of solutions for the class of quasilinear differential equations. This class contains model equations of nonlinear waves propagation: the nonlinear Schrödinger equation, the Korteweg--de Vries equation, and some others. 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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根据常系数线性微分方程的求解原理,通过一个适当变换,研究了一类变系数线性微分方程及其解的问题,从而可以得到这类方程在特征根都是互异单根时的解法和通解,并对三阶方程的各种情况进行了较为详尽的讨论. 相似文献
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S. A. Kashchenko 《Theoretical and Mathematical Physics》2018,195(3):807-824
For an initial differential equation with deviations of the spatial variable, we consider asymptotic solutions with respect to the residual. All solutions are naturally divided into classes depending regularly and irregularly on the problem parameters. In different regions in a small neighborhood of the zero equilibrium state of the phase space, we construct special nonlinear distribution equations and systems of equations depending on continuous families of certain parameters. In particular, we show that solutions of the initial spatially one-dimensional equation can be described using solutions of special equations and systems of Schr¨odinger-type equations in a spatially two-dimensional argument range. 相似文献
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Hongmei Zhang Fawang Liu 《高等学校计算数学学报(英文版)》2007,16(2):181-192
In this paper, the space-time Riesz fractional partial differential equations with periodic conditions are considered. The equations are obtained from the integral partial differential equation by replacing the time derivative with a Caputo fractional derivative and the space derivative with Riesz potential. The fundamental solutions of the space Riesz fractional partial differential equation (SRFPDE) and the space-time Riesz fractional partial differential equation (STRFPDE) are discussed, respectively. Using methods of Fourier series expansion and Laplace transform, we derive the explicit expressions of the fundamental solutions for the SRFPDE and the STRFPDE, respectively. 相似文献
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Existence of Solutions for Fractional
Integro-differential Equations with Impulsive and
Integral Conditions 下载免费PDF全文
This paper presents the existence of solutions for a class of Cauchy
problems with integral condition for impulsive fractional integro-differential
equations. Based on definition of solution for impulsive fractional integro-
differential equations, the existence theorems of solutions of fractional differ-
ential equation are obtained by applying fixed point methods. Finally, three
examples are given to demonstrate the feasibility of the obtained results. 相似文献