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1995 | 15 | 1 | 43-60
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Convergence results for nonlinear evolution inclusions

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In this paper we consider evolution inclusions of subdifferential type. First, we prove a convergence result and a continuous dependence proposition for abstract Cauchy problem of the form u' ∈ -∂⁻f(u) + G(u), u(0) = x₀, where ∂⁻f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in IR ∪ {+∞}, and G is a multifunction from C([0,T],Ω) into the nonempty subsets of L²([0,T],H). We obtain analogous results for the multivalued perturbed problem x' ∈ -∂⁻f(x) + G(t,x), x(0) = x₀, where G:[0,T]×Ω → N(H) is a suitable multifunction.
  • Department of Mathematics of Perugia University, Via Vanvitelli 1, Perugia 06123, Italy
  • Department of Mathematics of Perugia University, Via Vanvitelli 1, Perugia 06123, Italy
  • [1] J. P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin 1984.
  • [2] H. Brezis, Analyse fonctionelle, théorie et applications, Masson, Paris 1983.
  • [3] T. Cardinali, F. Papalini, Existence theorems for nonlinear evolution inclusions, to apper.
  • [4] G. Colombo, M. Tosques, Multivalued perturbations for a class of nonlinear evolution equations, Ann. di Mat. Pura Appl. 160 (1991), pp 147-162.
  • [5] J. Hale, Ordinary differential equations, Wiley-Interscience, New York 1969.
  • [6] M. Tosques, Quasi-autonomous parabolic evolution equations associated with a class of nonlinear operators, Ricerche di Matematica 38 (1989), pp. 63-92.
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