Well posedness for evolution inclusions. (1994) - Balachandran, K.; Anguraj, A.
Abstract : We prove the existence of a continuous selection of the multivalued map φ → Φ ( φ ) which is the set of all mild solutions of the evolution inclusion x ( t ) ∈ A x ( t ) + F ( t, x ( t ) ) + ∫ 0 t h ( t − s ) g ( x ( s ) ) d s x ( 0 ) = φ . Here F is a multivalued map, Lipschitzian with respect to x, and A is the infinitesimal generator of a C 0 -semigroup.