Nonlinear Impulsive Evolution Equations
نویسنده
چکیده
We study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive evolution equation u′(t) = Au(t) + f(t, u(t)), 0 < t < T0, t = ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, ..., 0 < t1 < t2 < ... < T0, in a Banach space X, where A is the generator of a strongly continuous semigroup, ∆u(ti) = u(t+i ) − u(ti ), and Ii’s are some operators. The impulsive conditions can be used to model more physical phenomena than the traditional initial value problems u(0) = u0. We apply the semigroup theory to first study the existence and uniqueness of the mild solutions, and then show that the mild solutions give rise to classical solutions if f is continuously differentiable. AMS (MOS) Subject Classification : 34G.
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