Existence and Uniqueness of Mild and Classical Solutions of Impulsive Evolution Equations
نویسندگان
چکیده
We consider the non-linear impulsive evolution equation u′(t) = Au(t) + f(t, u(t), Tu(t), Su(t)), 0 < t < T0, t 6= ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, 3, . . . , p. in a Banach space X, where A is the infinitesimal generator of a C0 semigroup. We study the existence and uniqueness of the mild solutions of the evolution equation by using semigroup theory and then show that the mild solutions give rise to a classical solutions.
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