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Controllability of Nonlinear Neutral Evolution Equations with nonlocal conditions

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Northeastern Mathematical Journal 2007年第2期23卷 115-122页

作者：刘明姬吕悦吕显瑞 School of Mathematics Jilin University Changchun 130012

In this paper, we establish sufficient conditions for the controllability of nonlinear neutral evolution equations with nonlocal conditions. The result is obtained by using Krasnoselski-Schaefer type fixed point theorem.

关键词： nonlocal condition nonlinear neutral evolution equation mild solution,Krasnoselski-Schaefer fixed point

GLOBALLY ATTRACTING SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS OF SOBOLEV TYPE

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Acta Mathematica Scientia 2017年第5期37卷 1295-1318页

作者： Van Hien LE Dinh Ke TRAN Trong Kinh CHU Department of Mathematics Hanoi National University of Education 136 Xuan ThuyCau GiayHanoiVietnam Department of Mathematics Hanoi Pedagogical University No.2VinhphucVietnam

We study a generalized Cauchy problem associated with a class of impulsive fractional differential inclusions of Sobolev type in Banach spaces. Our aim is to prove the existence of a compact set of globally attracting solutions to the problem in question. An application to fractional partial differential equations subject to impulsive effects is given to illustrate our results.

关键词： globally attracting solution impulsive condition nonlocal condition condensing map measure of non-compactness MNC-estimate

Existence of Semilinear Differential Equations with nonlocal Initial conditions

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Acta Mathematica Sinica,English Series 2007年第6期23卷 983-988页

作者： Xing Mei XUE Department of Mathematics Southeast University Nanjing 210096 P. R. China

In this paper we give the existence of mild solutions for semilinear Cauchy problems u′（t） = Au（t）＋f（t, u（t））, t ∈ I, a.e. with nonlocal initial condition u（O） = g（u）＋uo when the map g loses compactn... 详细信息

关键词： nonlocal condition compact semigroup mild solution

Measure of Noncompactness and Semilinear nonlocal Functional Differential Equations in Banach Spaces

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Acta Mathematica Sinica,English Series 2015年第1期31卷 140-150页

作者： Qi Xiang DONG Gang LI School of Mathematical Sciences Yangzhou University

This paper is concerned with the measure of noncompactness in the spaces of continuous functions and semilinear functional differential equations with nonloeal conditions in Banach spaces. The relationship between the Hausdorff measure of noncompactness of intersections and the modulus of equicontinuity is studied for some subsets related to the semigroup of linear operators in Banach spaces. The existence of mild solutions is obtained for a class of nonlocal semilinear functional differential equations without the assumption of compactness or equicontinuity on the associated semigroups Of linear operators.

关键词： Measure of noncompactness equicontinuity differential equation nonlocal condition C0-semigroup mild solution

EXISTENCE OF SOLUTIONS FOR nonlocal BOUNDARY VALUE PROBLEM OF FRACTIONAL DIFFERENTIAL EQUATIONS ON THE INFINITE INTERVAL

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Annals of Applied Mathematics 2017年第4期33卷 340-352页

作者： Abdellatif Ghendir Aoun Ecole Normale Superieure 16050 KoubaAlgiersAlgeria

In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of order a. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O＇Regan. Under a compactness criterion, the existence of solutions are established.

关键词： boundary value problem fractional differential equation infi-nite interval nonlocal condition fixed point theorem