Measures of noncompactness in spaces of regulated functions with application to semilinear measure driven equations

Cao, Yueju

doi:10.1186/s13661-016-0539-1

Cited by 19 publications

(9 citation statements)

References 28 publications

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“…Recently, the authors had discussed existence and exact controllability of semilinear measure driven equations in and , respectively. However, to the best of our knowledge, there have not been any results concerning with approximate controllability of abstract measure driven systems.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of semilinear measure driven systems

Cao

2018

Mathematische Nachrichten

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This paper investigates approximate controllability of semilinear measure driven equations in Hilbert spaces. By using the semigroup theory and Schauder fixed point theorem, sufficient conditions for approximate controllability of measure driven equations are established. The obtained results are a generalization and continuation of the recent results on this issue. Finally, an example is provided to illustrate the application of the obtained results.

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Section: Introductionmentioning

confidence: 99%

Approximate controllability of semilinear measure driven systems

Cao

2018

Mathematische Nachrichten

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“…Remark Let us note that our results are new even in the single‐valued case. We imposed different assumptions on the semigroup and on the function at the right‐hand side comparing to , .…”

Section: Resultsmentioning

confidence: 99%

“…As for the general framework, when the evolution part and the measure‐driven part are both involved in the dynamics of the system, as far as the authors know, only the single‐valued case has been taken into consideration (in , ). Interesting motivations for studying the semilinear measure driven problems can be found in .…”

Section: Introductionmentioning

confidence: 99%

Existence theory for semilinear evolution inclusions involving measures

Cichoń

Satco

2016

Mathematische Nachrichten

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We provide existence results for semilinear differential inclusions involving measures: trueleftdu∈Au0.28em0.28emdt+Ffalse(t,ufalse)0.28emdg0.28em,1emt∈false[0,1false],leftu(0)=u0,where A is the infinitesimal generator of a C0‐semigroup {T(t),t≥0} of contractions on a separable Banach space X and g:[0,1]→R is a right‐continuous non‐decreasing function. The existence of mild solutions, as well as the compactness of the solution set are obtained via Kakutani–Ky Fan's fixed point theorem in the space of regulated functions endowed with weak, respectively strong topologies. Some examples of special cases covered by our existence results have been included.

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“…As a result, it cannot simulate some complex phenomena, such as Zeno's behavior. However, the dynamic system with discontinuous trajectory is modeled by a measure differential equation or measure-driven equation [4][5][6][7][8][9][10]. Measure differential equations (MDEs) were studied in the early days [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%