On invariant sets and on a theorem of Ważewski
Abstract: The first part of the paper treats the question of the existence of a solution of an ordinary differential equation which exists for and remains in a given closed set F for every assigned initial point or, in the autonomous case, . The results involve conditions which, for the autonomous case, reduce to as for all . The second part of the paper deals with theorems of the Ważewski type which, in some situations, permit the relaxation of the hypothesis that egress points are strict egress points.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34A10
Retrieve articles in all journals with MSC: 34A10
Keywords: Invariant sets, trajectory derivative, Lyapunov, egress points
Article copyright: © Copyright 1972 American Mathematical Society