Precompactness of the Set of Trajectories of the Controllable System Described by a Nonlinear Volterra Integral Equation


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Huseyin A. , Huseyin N.

MATHEMATICAL MODELLING AND ANALYSIS, cilt.17, ss.686-695, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 17 Konu: 5
  • Basım Tarihi: 2012
  • Doi Numarası: 10.3846/13926292.2012.736088
  • Dergi Adı: MATHEMATICAL MODELLING AND ANALYSIS
  • Sayfa Sayıları: ss.686-695

Özet

In this paper the controllable system whose behaviour is described by a nonlinear Volterra integral equation, is studied. The set of admissible control functions is the closed ball of the space L-p (p > 1) with radius mu(0) and centered at the origin. It is shown that the set of trajectories of the system is a bounded and pre-compact subset of the space of continuous functions.