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      一類帶有逐段常變量的二階微分方程的概周期解

      2019-07-31 05:05:52姚慧麗張悅嬌侯盛楠
      關(guān)鍵詞:微分方程

      姚慧麗 張悅嬌 侯盛楠

      摘 要:基于微分方程的概周期解比周期解更具有一般性,本文將對(duì)一類帶有逐段常變量的二階微分方程的概周期解進(jìn)行研究。根據(jù)這類方程的解在整數(shù)點(diǎn)的連續(xù)性,構(gòu)造了一類非齊次差分方程。利用對(duì)應(yīng)的齊次差分方程的特征根,并借助于相應(yīng)的差分方程的概周期序列解和概周期函數(shù)以及概周期序列的一些性質(zhì),探討了這類方程的概周期解的存在性以及該類解的唯一性。

      關(guān)鍵詞:概周期解;概周期序列解;微分方程;差分方程;逐段常變量

      DOI:10.15938/j.jhust.2019.03.024

      中圖分類號(hào): O177.9

      文獻(xiàn)標(biāo)志碼: A

      文章編號(hào): 1007-2683(2019)03-0143-06

      Abstract:Almost periodic solutions of differential equations are more general? than periodic solutions, so almost periodic solutions will be studied on a class secondorder differential equations with piecewise constant argument. A class of nonhomogeneous difference equations are constructed by the continuity of solutions at the integer point of this class of equations. The existence of almost periodic solutions and the uniqueness of this kind of solutions on this class of equations are investigated by using of eigenvalue of corresponding homogeneous difference equations, almost periodic sequence solutions of relevant difference equations and some properties of almost periodic functions and almost periodic sequences.

      Keywords:almost periodic solutions; almost periodic sequence solutions; differential equations; difference equations; piecewise constant argument

      參 考 文 獻(xiàn):

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      [2] SHAH S M, WIENER J. Advanced Differential Equations with Piecewise Constant Argument Deviations[J]. Acta Math, 1983, (6): 671.

      [3] BOHR H. Zur Theorie Der Fastperiodischen[J]. Acta. Math., 1925, 45: 19.

      [4] FRECHET M. Les Functions Asymptotiquement Presque Periodiques[J]. Rev. Scientifique, 1941, 79: 341.

      [5] EBERLEIN W F. Abstract Ergodic Theorems and Weakly Almost Periodic Functions[J]. Amer. Math. Soc., 1949, 69: 217.

      [6] ZHANG C. Pseudoalmost Periodic Functions and Their Applications[D]. The University of Western Ontario, 1992: 55.

      [7] 樸大雄. 帶逐段常變量[t+1/2]的微分方程組的偽概周期解[J]. 中國(guó)科學(xué), 2003, 33(3):220.

      [8] YUAN RONG. A New Almost Periodic Type of Solutions of Second Order Neutral Delay Differential Equations with Piecewise Constant Argument[J]. Sci.China, 2003, 43(2): 371.

      [9] GUO JIANLIN, YUAN RONG. Pseudo Almost Periodic Solutions of A Singularly Perturbed Differential Equation with Piecewise Constant Argument[J]. Acta Math, 2007, 23(3): 423.

      [10]姚慧麗, 張娜, 薛寒. 一類具有逐段常變量擾動(dòng)系統(tǒng)的漸近概周期解. 哈爾濱理工大學(xué)學(xué)報(bào),2015,1:89.

      [11]王麗,張傳義. 帶逐段常變量的二階中立型延遲微分方程的概周期解[J]. 數(shù)學(xué)學(xué)報(bào), 2010, 53(2): 227.

      [12]常永奎, 成轉(zhuǎn)霞. 兩類隨機(jī)發(fā)展方程的偽概自守型解[D]. 蘭州交通大學(xué), 2014:1.

      [13]WU QIONG. MeanSquare Asymptotically Almost Automorphic Solutions to Fractional Stochastic Relaxation Equations[J]. International Journal of Differential Equations, 2015: 1.

      [14]袁榮. 具逐段常變量中立型時(shí)滯微分方程的概周期解[J]. 數(shù)學(xué)年刊, 1998, 499.

      [15]ZHANG HONG. Existence and Stability of Almost Periodic Solutions for CNNs with Continuously Distributed Leakage Delays[J]. Neural Comput and Applic, 2014, 24:1135.

      [16]XU YANLI. New Results on Almost Periodic Solutions for CNNs with Timevarying Leakage Delays[J]. Neural Comput and Applic, 2014, 25: 1293.

      [17]YUAN RONG. On the Spectrum of Almost Periodic Solution of SecondOrder Scalar Function Differential Equation with Piecewise Constant Argument[J]. J. Math. Anal. Appl., 2005, 303: 103.

      [18]楊淑芳, 王鑫. 二階中立型含逐段常滯量微分方程的偽概周期解的存在性[J].國(guó)防科技大學(xué)學(xué)報(bào), 2005, 27(3): 120.

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      (編輯:關(guān) 毅)

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