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一类线性微分方程的指数增长型伪概自守温和解

来源:用户上传      作者:姚慧丽 郭洺君 王晶囡 宋晓秋

  摘 要:微分方程是基于解决各种实际问题而建立的一种数学模型,对微分方程的一个主要研究方向是各种解的存在性问题。伪概自守函数是比概自守函数、渐近概自守函数更广的函数。本文将探讨一类指数增长型的伪概自守函数在一类线性微分方程中的应用,利用C0-半群以及这类函数的有关理论,研究此类型方程指数增长型的伪概自守温和解的存在问题以及唯一问题。
  关键词:微分方程;伪概自守温和解; 指数增长型;C0-半群
  DOI:10.15938/j.jhust.2020.01.021
  中图分类号: O175
  文献标志码: A
  文章编号: 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
  各种方程的概周期型解已被数学工作者进行了研究,如文[1-5]。1962年,S-Bochner将刻画概周期函数定义的条件变弱,给出了更广的一类函数的定义,即概自守函数[6]。G-M-N’Guerekata又先后对概自守和渐近概自守函数做了系统研究总结[7-8]。随后,梁进等人定义了伪概自守函数[9],且包含关系为
  {概自守函数}{渐近概自守函数}{伪概自守函数}
  这三类函数统称为概自守型函数。自此型函数理论建立以来,很多文献对各类微分方程的这种型的解存在问题进行了探讨[10-15]。特别近几年来,概自守型函数被学者们应用到了各种随机微分方程中,探究了这些方程的概自守型解的存在问题[16-20]。下列方程
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  (編辑:温泽宇)
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