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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Haddad, G. Monotone trajectories of differential inclusions and functional differential inclusions with memory. Israel J. Math. 39, 83–100 (1981). https://doi.org/10.1007/BF02762855
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DOI: https://doi.org/10.1007/BF02762855