Almost Periodic Type Solutions For A Class Of Delay Integral Equation And For A Class Of Stochastic Integral Differential Equation

Since the related theory of almost periodic type functions was put forward,it has attracted the attention of many scholars at home and abroad and have also studied it.Since then,scholars in many different fields have put forward the auto-conservative function and conducted in-depth research on it.In addition,the above two types of functions can be used to solve medical infectious disease problems in the medical field,and can also be used to solve problems such as celestial body motion in the field of astrophysics.These two types of functions often need to be combined with various types of integral and differential equations when solving.Therefore,this paper firstly explores the pseudo almost periodic solutions of a class of infinite delay integral equations.Secondly,the asymptotically almost periodic solutions of a class of stochastic integro-differential equations are explored.The following two parts of the study are reviewed in this paper:First,the first part explores the existence and uniqueness of pseudo almost periodic solutions for a class of infinite delay integral equations.However,before the main results are given,the related theories about the composition problem of pseudo almost periodic functions and the content of Krasnoselskii's fixed point theorem are introduced first.Finally,according to the related theory of pseudo almost periodic functions and some related assumptions,combined with Krasnoselskii's fixed point theorem,the existence and uniqueness of the pseudo almost periodic solutions of the equation is explored.Secondly,the second part explores the existence and uniqueness of the mean square asymptotically almost periodic solutions of a class of stochastic integro-differential equations.However,before the main results are given,the related concepts of the family of presolved operators included in the equation are given,and some related theories of the mean square asymptotically almost periodic functions compound problem are further given.Finally,combined with the Banach fixed point principle and some relevant assumptions of the mean square asymptotically almost periodic functions,the existence and uniqueness of the mean square asymptotically almost periodic mild solution of the equation is explored.