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One-sided Perron Differential Inclusions

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Abstract

The main qualitative properties of the solution set of almost lower (upper) semicontinuous one-sided Perron differential inclusion with state constraints in finite dimensional spaces are studied. Using the technique introduced by Veliov (Nonlinear Anal 23:1027–1038, 1994) we give sufficient conditions for the solution map of the above state constrained differential inclusion to be continuous in the sense of Hausdorff metric. An application on the propagation of the continuity of the state constrained minimum time function associated with the nonautonomous differential inclusion and the target zero is given. Some relaxation theorems are proved, which are used afterward to derive necessary and sufficient conditions for invariance.

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Authors and Affiliations

  1. Department of Mathematics, University Al. I. Cuza, Iaşi, 700506, Romania

    Tzanko Donchev & Alina Ilinca Lazu

  2. Abdus Salam School of Mathematical Sciences, 68-B New Muslim Town, Lahore, Pakistan

    Tzanko Donchev & Ammara Nosheen

  3. Department of Mathematics, Gh. Asachi Technical University, Iaşi, 700506, Romania

    Alina Ilinca Lazu

Authors
  1. Tzanko Donchev
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  2. Alina Ilinca Lazu
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  3. Ammara Nosheen
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Correspondence to Tzanko Donchev.

Additional information

Research of first and 2nd authors is supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0154, while research of 3rd author is partially supported by Higher Education Commission, Pakistan.

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Donchev, T., Lazu, A.I. & Nosheen, A. One-sided Perron Differential Inclusions. Set-Valued Var. Anal 21, 283–296 (2013). https://doi.org/10.1007/s11228-012-0227-y

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  • DOI: https://doi.org/10.1007/s11228-012-0227-y

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