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Existence of Mild Solutions for a Class of Fractional Non-autonomous Evolution Equations with Delay

Acta Mathematicae Applicatae Sinica 2020年第4期36卷 870-878页

作者： Bo ZHU Bao-yan HAN Wen-guang YU School of Mathematics and Quantitative Economics Shandong University of Finance and EconomicsJinan 250014China Common Course Teaching Department Shandong University of Art and DesignJinan 250014China School of Insurance Shandong University of Finance and EconomicsJinan 250014China

In this paper,we consider the existence and uniqueness of the mild solutions for a class of fractional non-autonomous evolution equations with delay and Caputo's fractional *** using the measure of noncompactness.β-resolvent family,fixed point theorems and Banach contraction mapping principle,we improve and generalizes some related results on this *** last,we give an example to illustrate the application of the main results of this paper.

关键词： Fractional non-autonomous evolution equations β-resolvent family Mild solution measure of noncompactness.

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RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

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Acta Mathematica Scientia 2014年第2期34卷 546-556页

作者： Bilel KRICHEN Department of Mathematics Preparatory Engineering Institute

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.

关键词： Demicompact linear operator relative essential spectrum Fredholm and semi-Fredholm operators measure of noncompactness.

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Positive Solutions for the Initial Value Problems of Impulsive Evolution Equations

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Journal of Mathematical Research and Exposition 2011年第6期31卷 1047-1056页

作者： He YANG Department of Mathematics Northwest Normal UniversityGansu 730070P.R.China

This paper deals with the existence of e-positive mild solutions（see Definition 1）for the initial value problem of impulsive evolution equation with noncompact semigroup u（t）＋ Au（t）= f（t,u（t））,t ∈ [0,＋∞）,t = tk,u-t=tk = Ik（u（tk））,k = 1,2,...,u（0）= x0 in an ordered Banach space *** using operator semigroup theory and monotonic iterative technique,without any hypothesis on the impulsive functions,an existence result of e-positive mild solutions is obtained under weaker measure of noncompactness.condition on nonlinearity of ***,an existence result without using measure of noncompaceness condition is presented in ordered and weakly sequentially complete Banach spaces,which is very convenient for *** example is given to illustrate that our results are more valuable.

关键词： impulsive evolution equation e-positive mild solution equicontinuous semigroup measure of noncompactness.

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Positive Solutions for a Second-Order Nonlinear Impulsive Singular Integro-Differential Equation with Integral Conditions in Banach Spaces

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Journal of Mathematical Research with Applications 2012年第5期32卷 599-614页

作者： Xingqiu ZHANG School of Mathematics,Liaocheng University,Shandong 252059,P.R.China School of Mathematics Liaocheng University Shandong 252059

The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point ... 详细信息

关键词： impulsive singular integro-differential equation positive solution M¨onch fixed point theorem measure of noncompactness.

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