A semilinear multivalued evolution equation is considered in a reflexive Banach space. The nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. No strong compactness is assumed, neither on the evolution operator generated by the linear part, or on the nonlinear term. A wide family of nonlocal associated boundary value problems is investigated by means of a fixed point technique. Applications are given to an optimal feedback control problem, to a nonlinear hyperbolic integro-differential equation arising in age-structure population models, and to a multipoint boundary value problem associated to a parabolic partial differential equation.

Nonlocal semilinear evolution equations without strong compactness: theory and applications / Irene, Benedetti; Malaguti, Luisa; Taddei, Valentina. - In: BOUNDARY VALUE PROBLEMS. - ISSN 1687-2770. - ELETTRONICO. - 60(2013), pp. 1-18.

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