caa a22 4500 477091598 CHVBK 20180405111516.0 cr unu---uuuuu 170330e19960601xx s 000 0 eng 10.1007/BF01195914 doi (NATIONALLICENCE)springer-10.1007/BF01195914 Nonlinear systems with unbounded controls and state constraints: a problem of proper extension [Elektronische Daten] [Monica Motta, Franco Rampazzo] We study a space-time extension of the notion of solution to a nonlinear control system with unbounded controls (in the form of derivatives) and state constraints. A natural motivation is provided by minimum problems, where the presence of unbounded controls together with the lack of any coercivity assumption may give rise to minimizing sequences of trajectories which converge to discontinuous maps. The main problem focused on in this paper can be summarized as follows: is the proposed extension a proper extension? Which means: is one able to approximate an extended trajectory with ordinary ones? When the system is subject to a state constraint the answer is generally negative. On the other hand, we prove that under suitable conditions on the vectogram at the boundary points of the constraint set the extension turns out to be proper. Birkhäuser Verlag, 1996 Motta Monica Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131, Padova, Italy aut Rampazzo Franco Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131, Padova, Italy aut Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/2(1996-06-01), 191-216 1021-9722 3:2<191 1996 3 30 https://doi.org/10.1007/BF01195914 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01195914 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Motta Monica Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131, Padova, Italy aut NATIONALLICENCE 700 1- Rampazzo Franco Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, 35131, Padova, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/2(1996-06-01), 191-216 1021-9722 3:2<191 1996 3 30 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer