Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions

Guo, Mengshu; Xue, Xingmei; Li, R.

doi:10.1023/b:jota.0000015688.53162.eb

Cited by 41 publications

(15 citation statements)

References 17 publications

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“…The methods are similar to that of Liu [3]. Thus, our results are extended those of Liu [3], Guo et al [10] and Benchohra et al [1]. This paper will be organized as follows.…”

Section: (T)−g(t X T )] ∈ Ax(t)+bu(t)+f(t X T ) T∈ J = [0t] T supporting

confidence: 72%

“…Benchohra and Ouahab [9] proved the existence of solutions for initial and boundary problems for second-order impulsive functional differential inclusions in Banach spaces. Guo et al [10] studied the controllability of impulsive evolutions inclusions with nonlocal conditions. Moreover, Benchohra et al [1] investigated the controllability of first-order semilinear impulsive functional differential inclusions.…”

Section: (T)−g(t X T )] ∈ Ax(t)+bu(t)+f(t X T ) T∈ J = [0t] T mentioning

confidence: 99%

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

Park

Kang

2009

Math. Meth. Appl. Sci.

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In this paper, we shall prove the controllability of second-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multi-valued mappings. As an example, we also consider an second-order impulsive neutral functional differential equation with infinite delay.

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“…The methods are similar to that of Liu [3]. Thus, our results are extended those of Liu [3], Guo et al [10] and Benchohra et al [1]. This paper will be organized as follows.…”

Section: (T)−g(t X T )] ∈ Ax(t)+bu(t)+f(t X T ) T∈ J = [0t] T supporting

confidence: 72%

Section: (T)−g(t X T )] ∈ Ax(t)+bu(t)+f(t X T ) T∈ J = [0t] T mentioning

confidence: 99%

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

Park

Kang

2009

Math. Meth. Appl. Sci.

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“…Recently, the problems of the controllability of differential systems and integrodifferential systems in Banach spaces were considered by many researchers, see for instance [3,6,13] and the references therein. In the case of the nonlocal condition, the semilinear evolution inclusions has been studied by Benchohra et al [7], Guo et al [17], Li and Xue [19]. for some f ∈ S F,x .…”

Section: Applicationmentioning

confidence: 99%

On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

Zhang¹

2012

OpMath

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“…And impulsive differential equations and inclusions dealing with control theory were investigated by [2,11,25]. Indeed, the first motivation of the study of the concept of differential inclusions comes from the development of some studies in control theory.…”

Section: Application To Control Theorymentioning

confidence: 99%

Existence and solution sets of impulsive functional differential inclusions with multiple delay

Helal¹,

Ouahab²

2012

OpMath

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Abstract. In this paper, we present some existence results of solutions and study the topological structure of solution sets for the following first-order impulsive neutral functional differential inclusions with initial condition:where J := [0, b] and 0 = t0 < t1 < . . . < tm < tm+1 = b (m ∈ N * ), F is a set-valued map and g is single map. The functions I k characterize the jump of the solutions at impulse points t k (k = 1, . . . , m). Our existence result relies on a nonlinear alternative for compact u.s.c. maps. Then, we present some existence results and investigate the compactness of solution sets, some regularity of operator solutions and absolute retract (in short AR). The continuous dependence of solutions on parameters in the convex case is also examined. Applications to a problem from control theory are provided.

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Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions

Cited by 41 publications

References 17 publications

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

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

On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

Existence and solution sets of impulsive functional differential inclusions with multiple delay

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