G. Gabor, M. Quincampoix
"On attainability of a set by at least one solution to a differential inclusion."
In many dynamical systems problems, it is interesting to know not
only that an equilibria do exist but also to know if the
equilibria can be reached by at least one trajectory (possibly
asymptotically). It is worth pointing out that this question is
different from those of stability, or attractiveness of the
equilibria. In the present paper, our purpose is to give
sufficient conditions for answering positively to the above
question. More generally we address the question of attainability
of a closed set E by at least one trajectory starting
from outside E. Our method is based on a kind of Lyapunov
Analysis based on Viability Theory and topological methods.