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TABLE DES MATIÈRESIntroduction .....................................................................................................5I. PréliminairesI.1. Notations et définitions.............................................................................7I.2. Espaces de Sobolev.................................................................................8I.3. Transversalité topologique .....................................................................10II. Intervalle d'existence de...
Abstract. Applying the topological transversality method of Granas and the a priori bounds technique, we prove some existence theorems for diflerential inclusions of the form x" ∈ F(t, x, x'), x ∈ ℬ, where F is a Carathéodory multifunction with convex, compact values. No growth condition will be imposed on F.
We study semilinear equations and inequalities of parabolic type with discontinuous nonlinearities, possibly subjected to convex or even nonconvex constraint conditions. To prove some existence theorems we regard the solutions as «curves of maximal relaxed slope» for a suitable functional on the given constraint.
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