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Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces

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Abstract

In this note, we establish a sufficient condition for the controllability of a first-order semilinear differential system with nonlocal initial conditions in Banach spaces. The approach used is the Sadovskii fixed-point theorem combined with operator semigroups. Particularly, the compactness of the operator semigroups is not needed in this article.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, P.R. China

    Y. K. Chang

  2. Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain

    J. J. Nieto

  3. Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, P.R. China

    W. S. Li

Authors
  1. Y. K. Chang
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  2. J. J. Nieto
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  3. W. S. Li
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Corresponding author

Correspondence to Y. K. Chang.

Additional information

Communicated by F. Zirilli.

Y.K. Chang was supported by Tianyuan Youth Fund of Mathematics in China (10826063), NNSF of China (10801065), the Scientific Research Fund of Gansu Provincial Education Department (20868), and Qing Lan Talent Engineering Funds (QL-05-16A) of Lanzhou Jiaotong University.

J.J. Nieto was supported by Ministerio de Educacion y Ciencia-FEDER Project MTM2007-61724, and by Xunta de Galicia-FEDER Project PGIDIT05PXIC20702PN.

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Chang, Y.K., Nieto, J.J. & Li, W.S. Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces. J Optim Theory Appl 142, 267–273 (2009). https://doi.org/10.1007/s10957-009-9535-2

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