Monotone trajectories of differential inclusions and functional differential inclusions with memory |
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Authors: | Georges Haddad |
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Affiliation: | (1) Ceremade Université de Paris — Dauphine, Paris, France |
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Abstract: | The paper gives a necessary and sufficient condition for the existence of monotone trajectories to differential inclusionsdx/dt ∈S[x(t)] defined on a locally compact subsetX ofR p, the monotonicity being related to a given preorder onX. This result is then extended to functional differential inclusions with memory which are the multivalued case to retarded functional differential equations. We give a similar necessary and sufficient condition for the existence of trajectories which reach a given closed set at timet=0 and stay in it with the monotonicity property fort≧0. |
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