Controllability of Semilinear Evolution Equations with Nonlocal Conditions

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.     

Semilinear Differential Inclusions in Separable Banach Spaces

Ｓｅｍｉｌｉｎｅａｒ　Ｄｉｆｆｅｒｅｎｔｉａｌ　Ｉｎｃｌｕｓｉｏｎｓ　ｉｎ　Ｓｅｐａｒａｂｌｅ　Ｂａｎａｃｈ　ＳｐａｃｅｓＸｕｅＸｉｎｇｍｅｉ（薛星美）ａｎｄＳｏｎｇＧｕｏｚｈｕ（宋国柱）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎａｎｊｉｎ...     

On Impulsive Hyperbolic Differential Inclusions with?Nonlocal Initial Conditions

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases. Y.-K. Chang was supported by “Qing Lan” Talent Engineering Funds (QL-05-16A), by Lanzhou Jiaotong University, the Scientific Research Fund of Gansu Provincial Education Department (0704-14). J.J. Nieto was supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.     

Controllability of Nonlinear Neutral Evolution Equations with Nonlocal Conditions

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.     

Controllability for Semilinear Functional and Neutral Functional Evolution Equations with Infinite Delay in Fréchet Spaces

The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Fréchet spaces, combined with the semigroup theory.     

Convergence of a Hybrid Projection Algorithm in Banach Spaces

In this paper, we consider a hybrid projection algorithm for two families of quasi-φ-nonexpansive mappings. We establish strong convergence theorems of common fixed points in the framework of Banach spaces. Our results improve and extend the corresponding results announced by many others.     

Some Uniqueness Results for Functional Damped Semilinear Differential Equations in Frechet Spaces

A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas （Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec 22, （2）, 161-168 （1998））, combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first- and second-order functional semi linear and neutral damped differential equations in Frechet space.     

Null Controllability with Constraints on the State for the Semilinear Heat Equation

We consider a null controllability problem for the semilinear heat equation with finite number of constraints on the state. Interpreting each constraint by means of adjoint state notion, we transform the linearized problem into an equivalent linear problem of null controllability with constraint on the control. Using inequalities of observability adapted to the constraint, we solve the equivalent problem. Then, by a fixed-point method, we prove the main result.     

Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces

We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator.     

Bifurcation Theorems in Orderd Banach Spaces With Applications to Semilinear Elliptic Equations

Let X be a ordered Banach space,P a positive cone in X and O∑QX abounded open set.We consider the following equations. (1)x-L(x)-g(x)-h(λ,x)=0, (2)x-L(x)-λg(x)-h(λ,x)=0,where we suppose that     

非局部半线性积微分系统的可控制性

本文运用半群理论和Schauder不动点定理,在Banach空间研究了一类非局部半线性积微分系统的可控制性.最后,举例说明了所得结果.     

Controllability results for nondensely defined evolution differential inclusions with nonlocal conditions

In this paper we prove controllability results for some semilinear nondensely defined evolution differential inclusions in Banach spaces with nonlocal conditions.     

On controllability of fractional impulsive neutral infinite delay evolution integrodifferential systems in Banach spaces

In this work, controllability of fractional impulsive neutral evolution integrodifferential systems in a Banach space has been addressed. Sufficient conditions for the controllability are established using fractional calculus, resolvent operators and Krasnoselskii’s fixed point theorem.     

Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order

In this paper, we prove some existence and uniqueness of mild solutions for a semilinear integrodifferential equation of fractional order with nonlocal initial conditions in α-norm. We assume that the linear part generates a noncompact analytic semigroup. Our results cover the cases that the nonlinearity F takes values in different spaces such as X,X_α and X_β, where α≤β(0,1). Finally, some practical consequences are also obtained.     

Controllability of second-order neutral functional differential inclusions in Banach spaces

In this paper, we prove the controllability of second-order neutral functional differential inclusions in Banach spaces. The result are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for condensing maps due to Martelli.     

Controllability of impulsive differential systems with nonlocal conditions

The paper is concerned with the controllability of impulsive functional differential equations with nonlocal conditions. Using the measure of noncompactness and Mönch fixed-point theorem, we establish some sufficient conditions for controllability. Firstly, we require the equicontinuity of evolution system, and next we only suppose that the evolution system is strongly continuous. Since we do not assume that the evolution system generates a compact semigroup, our theorems extend some analogous results of (impulsive) control systems.     

Remarks on the paper “Controllability of second order differential inclusion in Banach spaces” [J. Math. Anal. Appl. 285 (2003) 537-550]

An error is pointed out in the paper [J.R. Kang, Y.C. Kwun, J.Y. Park, Controllability of second order differential inclusion in Banach spaces, J. Math. Anal. Appl. 285 (2003) 537-550]. By an additional condition the considered system is controllable.