非自治中立型无穷时滞泛函微分方程的加权伪概自守解

首先引入h型Stepanov 加权伪概自守函数和∞型Stepanov加权伪概自守函数的概念, 接着建立了其函数空间的完备性以及相应组合定理, 最后证明了一类非自治无穷时滞偏中立型泛函微分方程在S^p-加权伪概自守系数下加权伪概自守解的存在唯一性.     

Banach空间中非线性Volterra积分方程及其应用

本文以非紧致测度为工具研究了Banach空间中的非线性Volterra积分方程,我们得到一些存在性定理,其实质是取消了核函数的一致连续性。我们也得到解集对参数的上半连续依赖性的结果。最后,利用所得结果我们给出了一个半线性发展方程的mild解的存在性。     

广义Volterra积分方程解的存在性

本文考虑Ｂａｎａｃｈ空间是形如ｘ（ｔ）＝ｕ（ｔ）＋∫_Gtf(t,s,x(s))ds的广义Ｖｏｌｔｅｒｒａ积分方程，利用Ｍ?ｎｃｈ不动点定理得到所论方程解的某些存在定理．     

一个减算子不动点定理及其对非线性Volterra型积分方程的应用

利用锥理论,在不需要上下解的条件下,获得一个新的减算子不动点定理,推广了最近文献的结果;并给出Banach空间中非线性Volterra型积分方程解的唯一性.     

广义模糊Volterra积分方程与强模糊Henstock积分

研究形如的模糊Volterra积分方程整体解的存在性.这里h,k,g是实值函数,f为强模糊Henstock可积的模糊数值函数.所用的方法和工具是利用模糊数值函数的等度可积性和非紧性测度的性质以及广义Darbo不动点定理.     

线性非卷积型Volterra积分方程和积分微分方程的周期解

其中g,q,x,y,f∈R~n,A,C,D为n×n矩阵。假设A(t),f(t)在(-∞,∞)上连续,C,D当-∞>s,t<∞为连续。 本文的主要进展是建立了这些方程的周期解表达公式。在非卷积情况下,文献中仅见T.A.Burton[1]就方程(0.4)当D≡0时给出的一个周期解公式:     

含多重积分的Volterra型积分方程与不等式

本文考虑一定有序局部紧空间上含多重积分的Ｖｏｌｔｅｒｒａ型积分方程，给出了此类方程可解的充分条件，建立了相应的积分不等式．本文结果包含许多已知结论作为特殊情况．     

Volterra积分方程和泛函微分方程的振动性

本文建立了Ｖｏｌｔｅｒａ积分方程和一阶泛函微分方程解的振动准则．     

随机Volterra积分方程的非标准及演解法

本文借助星型Ｍｏｂｉｕｓ反演得到随机积分Ｖｏｌｔｅｒｒａ方程的一个全新解法．它旨在揭示离散反演与连续反演的内在联系，为探索各类反演的统一性提供了一种可能的研究途径．     

严格单调函数与Riemann积分有关的一些性质

下面的讨论都是对严格递增函数进行的(严格递减函数可同样讨论,以后遇到的函数f(x)均指严格递增函数)。首先给出一定理,它在一定程度上可看作是微分中值定理之逆。     

Some properties of Stepanov-like almost automorphic functions and applications to abstract evolution equations

This article is concerned with some properties of Stepanov-like almost automorphic (S ^p -a.a.) functions. We establish a composition theorem about S ^p -a.a. functions, and with its help, study the existence and uniqueness of almost automorphic solutions for semilinear evolution equations in Banach spaces. Moreover, integration and differentiation of S ^p -a.a. functions are discussed. Some theorems extend earlier results.     

Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations

In this paper, we establish a new composition theorem about Stepanov-like pseudo almost automorphic functions under the local Lipschitz condition. Using this composition theorem, we also study the existence and uniqueness of pseudo almost automorphic solutions for nonautonomous evolution equations. Our results extend many recent known ones on these topics.     

On Stepanov-like (pseudo) almost automorphic functions

We prove new composition theorems for Stepanov-like almost automorphic and Stepanov-like pseudo-almost automorphic functions. An application is given to a class of evolution equations with Stepanov-like pseudo-almost automorphic perturbations.     

Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations

We establish new theorems for the composition of pseudo almost periodic and pseudo almost automorphic functions in Banach spaces. Our results extend the recent ones [H. Li, F. Huang and J. Li, Composition of pseudo almost-periodic functions and semilinear differential equations, J. Math. Anal. Appl. 255 (2001), pp. 436–446; J. Liang, J. Zhang, T.J. Xiao, Composition of pseudo almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl. 340 (2001), pp. 1493–1499]. We also study some sufficient conditions for the continuity of the superposition operator. As an application to the abstract results, we give some existence theorems of pseudo almost periodic/automorphic solutions for some semilinear evolution equations and examples with the heat equation.     

Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations

In this paper, applying the theory of semigroups of operators to evolution family and Banach fixed point theorem, we prove the existence and uniqueness of an (a) almost automorphic (weighted pseudo almost automorphic) mild solution of the semilinear evolution equation x^′(t)=A(t)x(t)+f(t,x(t)) in Banach space under conditions.     

Composition of pseudo almost automorphic and asymptotically almost automorphic functions

This paper is concerned with pseudo almost automorphic functions, which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions. New results, concerning the composition of pseudo almost automorphic functions, are established.     

Weighted pseudo almost automorphic functions and WPAA solutions to semilinear evolution equations

In this paper, we reveal several basic properties about nonlinear vector-valued weighted pseudo almost automorphic functions, including equivalence, completeness, translation invariance, composition theorem, and convolution theorem of these functions. We also give some concrete examples to illustrate our results. Finally, we obtain a new existence theorem of nonlinear weighted pseudo almost automorphic solutions for semilinear evolution equations in Banach spaces.