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    一類線性微分方程的指數(shù)增長型偽概自守溫和解

    2020-05-21 03:31:21姚慧麗郭洺君王晶囡宋曉秋
    關(guān)鍵詞:微分方程

    姚慧麗 郭洺君 王晶囡 宋曉秋

    摘 要:微分方程是基于解決各種實際問題而建立的一種數(shù)學(xué)模型,對微分方程的一個主要研究方向是各種解的存在性問題。偽概自守函數(shù)是比概自守函數(shù)、漸近概自守函數(shù)更廣的函數(shù)。本文將探討一類指數(shù)增長型的偽概自守函數(shù)在一類線性微分方程中的應(yīng)用,利用C0-半群以及這類函數(shù)的有關(guān)理論,研究此類型方程指數(shù)增長型的偽概自守溫和解的存在問題以及唯一問題。

    關(guān)鍵詞:微分方程;偽概自守溫和解; 指數(shù)增長型;C0-半群

    DOI:10.15938/j.jhust.2020.01.021

    中圖分類號: O175

    文獻(xiàn)標(biāo)志碼: A

    文章編號: 1007-2683(2020)01-0140-04

    Abstract:Differential equations are a kind of mathematical models which have been established to solve all kinds of practical problemsThe existence problems of various solutions for differential equations are a main research directionPseudo almost automorphic functions are more wide functions than almost automorphic functions and asymptotically almost automorphic functions-The applications of exponentiauy type pseudo almost automorphic f unctions on a class of linear differential equations will be investigated, the existence problems and uniqueness problems of exponentiauy type pseudo almost automorphic mild solution of this type equations are researched by using some related theories of C0-semigroup and this type i functions in this paper-

    Keywords:differential equations; pseudo almost automorphic mild solution; exponentiauy type; C0-semigroup

    0 引 言

    各種方程的概周期型解已被數(shù)學(xué)工作者進(jìn)行了研究,如文[1-5]。1962年,S-Bochner將刻畫概周期函數(shù)定義的條件變?nèi)?,給出了更廣的一類函數(shù)的定義,即概自守函數(shù)[6]。G-M-NGuerekata又先后對概自守和漸近概自守函數(shù)做了系統(tǒng)研究總結(jié)[7-8]。隨后,梁進(jìn)等人定義了偽概自守函數(shù)[9],且包含關(guān)系為

    {概自守函數(shù)}{漸近概自守函數(shù)}{偽概自守函數(shù)}

    這三類函數(shù)統(tǒng)稱為概自守型函數(shù)。自此型函數(shù)理論建立以來,很多文獻(xiàn)對各類微分方程的這種型的解存在問題進(jìn)行了探討[10-15]。特別近幾年來,概自守型函數(shù)被學(xué)者們應(yīng)用到了各種隨機(jī)微分方程中,探究了這些方程的概自守型解的存在問題[16-20]。下列方程

    參 考 文 獻(xiàn):

    [1] 姚慧麗,顏榮.一類差分方程的漸近概周期序列解的存在性[J].哈爾濱理工大學(xué)學(xué)報,2010,15(6):59.

    YAO Huili, YAN Rong. Existence of Asymptotic Almost Periodic Sequence Solution of a Difference Equation[J]. Journal of Harbin University of Science and Technology. 2010, 15(6): 59.

    [2] YOSHIHIRO HAMAYA. Bifurcation of Almost Periodic Solutions in Difference Equations[J]. Journal of Difference Equations and Applications, 2004, 10(3): 257.

    [3] 許廣濤,姚慧麗.一類時滯積分方程的漸近概周期解的存在性[J].哈爾濱理工大學(xué)學(xué)報,2008,13(1):106.

    XU Guangtao, YAO Huil. Existence of Asymptotically Almost Periodic Solution in a Certain Delay Integral Equation[J]. Journal of Harbin University of Science and Technology. 2008, 13(1): 106.

    [4] DIAGANA T. Weighted Pseudo Almost Periodic Solutions to Some Differential Equations[J]. Nonlinear Anal. Theory Methods Appl, 2008, 68: 2250.

    [5] 莊榮坤, 吳洪武, 張留偉. 一類三階逐段常變量微分方程漸近概周期解[J]. 高校應(yīng)用數(shù)學(xué)學(xué)報,2012,27(2):157.

    ZHUANG Rongkun, WU Hongwu, ZAHNG Liuwei. Asymptotic Almost Periodic Solutions of Third-order Neutral Differential Equations with Piecewise Constant Argument[J]. Applied Mathematics A Journal of Chinese Universities. 2012, 27(2): 157.

    [6] BOCHNER S. A New Approach to Almost-periodicity[J]. Proc. Nat. Acad. Sci. USA ,1962,48:2039.

    [7] NGUEREKATA G M. Almost Automorphic Functions and Amost Periodic Functions in Abstract Spaces[M]. K1uwer Academic/Plnum Publishers,New York-Bedin-Moscow,2001.

    [8] DIAGANA T, NGUEREKATA G M. Amost Automorphic Solutions to Some Classes of Partial Evolution Equations[J]. Appl.Math.Lett.,2007,20(4):462.

    [9] LIANG Jin, ZHANG Jun and XIAO TiJun. Composition of Pseudo Almost Automorphic and Asymptotically Amost Automorphic Functions[J]. Math.Anal.Appl. 2008, 340(2):1493.

    [10]SONG Xiaoqiu. Almost Automorphic and Pseudo Almost Automorphic Solutions of Semilinear Differential Equations[J]. Acta Analysis Functionalis Applicata, 2009, 11(4) :52.

    [11]GISELE M M,GASTON M N. Almost Automorphic Solutions of Neutral Functional Differential Equations[J]. Electronic Journal of Differential Equation, 2010(69):1.

    [12]張蕊,常永奎,NGUEREKATA G M.非自治中立型無窮時滯泛函微分方程的加權(quán)偽概自守解[J].中國科學(xué):數(shù)學(xué),2013,43(3):273.

    ZHANG Rui, CHANG Yongkui, NGUEREKATA G M. Weighted Pseudo Almost Automorphic Solutions for Non-Autonomous Neutral Functional Difffferential Equations with Infifinite Delay[J]. Scientia Sinica(Mathematica). 2013, 43(3): 273.

    [13]劉敬懷,宋曉秋,陸鳳玲.半線性微分方程的概自守與偽概自守解[J].應(yīng)用泛函分析學(xué)報,2009,11(4):294.

    LIU Jinghuai, SONG Xiaoqiu, LIU Fengling. Almost Automorphic and Pseudo Almost Automorphic Solutions of Semilinear Diff erential Equations[J]. Acta Analysis Functionalis Applicata. 2009, 11(4): 294.

    [14]肖體俊,梁進(jìn),張俊.偽概自守函數(shù)及在發(fā)展方程中的應(yīng)用[J]. 中國科學(xué)技術(shù)大學(xué)學(xué)報,2009(45):64.

    XIAO Tijun, LIANG Jin, ZHANG Jun. Pseudo Almost Automorphic Functions and Applications to Evolution Equations[J]. Journal of University of Science and Technology of China. 2009, 45: 64.

    [15]張榮娟,褚衍彪,宋曉秋.抽象微分方程的加權(quán)偽概自守解[J].棗莊學(xué)院學(xué)報,2010(34):45.

    ZHANG Rongjuan, CHU Yanbiao, SONG Xiaoqiu. Weighted Pseudo Almost Automorphic Solutions of Abstract Integral Equation[J]. Journal of Zaozhuang University, 2010, 34: 45.

    [16]DIOP M A, EZZINBI K, MBAYE M M. Existence and Global Attractiveness of a Square-mean μ-pseudo Almost Automorphic Solution for Some Stochastic Evolution Equation Driven by Lévy Noise[J]. Mathematische Nachrichten, 2016, 290(8/9):1260.

    [17]GU Y, REN Y, SAKTHIVEL R. Square-mean Pseudo Almost Automorphic Mild Solutions for Stochastic Evolution Equations Driven by G-Brownian Motion[J]. Stochastic Analysis & Applications, 2016, 34(3):528.

    [18]XI LIANG, YU LIANG, BAIFENG. Square-mean Almost Automorphic Solutions to Some Stochastic Evolution Equations I: Autonomous Case[J]. Acta Mathematica Applicatae Sinica, English Series, 2015, 31(3): 577.

    (編輯:溫澤宇)

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