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...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 compactness in Banach spaces.展开更多
In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonloc...In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.展开更多
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...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.展开更多
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.
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...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.展开更多
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 orde...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.展开更多
In this paper we examine the controllability problems of certain evolution equations with nonlocal conditions. Using the Schaefer fixed-point theorem, we obtain sufficient conditions for controllability and we give an...In this paper we examine the controllability problems of certain evolution equations with nonlocal conditions. Using the Schaefer fixed-point theorem, we obtain sufficient conditions for controllability and we give an application.展开更多
文摘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 compactness in Banach spaces.
基金supported by NSF of China (11171110)Shanghai Leading Academic Discipline Project (B407)
文摘In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.
基金supported by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under grant number 101.02-2015.18
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271316 and 11201410)Natural Science Foundation of Jiangsu Province(Grant No.BK2012260)
文摘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.
文摘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.
文摘In this paper we examine the controllability problems of certain evolution equations with nonlocal conditions. Using the Schaefer fixed-point theorem, we obtain sufficient conditions for controllability and we give an application.
