Scopo della presente Nota è quello di fornire una maggiorazione della lunghezza dell'intervallo sul quale il problema (1) (2) (3) ammette soltanto la soluzione nulla.
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
We consider a nonconvex and nonclosed second-order evolution inclusion and we prove the arcwise connectedness of the set of its mild solutions.
We prove that the solutions of a sweeping process make up an -set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.
In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results.