Open AccessPRECOMPACTNESS OF THE SET OF TRAJECTORIES OF THE CONTROLLABLE SYSTEM DESCRIBED BY A NONLINEAR VOLTERRA INTEGRAL EQUATION
Author(s) -
Anar Hüseyin,
Nesir Hüseyin
Publication year - 2012
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2012.736088
Subject(s) - mathematics , nonlinear system , bounded function , ball (mathematics) , set (abstract data type) , volterra integral equation , mathematical analysis , space (punctuation) , integral equation , volterra equations , closed set , radius , computer science , physics , quantum mechanics , programming language , operating system , computer security
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 µ 0 and centered at the origin. It is shown that the set of trajectories of the system is a bounded and precompact subset of the space of continuous functions.