Perturbation method for nonlocal impulsive evolution equations. (English) Zbl 1257.93034
Summary: This paper deals with the existence of mild solutions for a class of semilinear nonlocal impulsive evolution equations in ordered Banach spaces. The existence and uniqueness theorem of a mild solution for the associated linear nonlocal impulsive evolution equation is established. With the aid of the theorem, the existence of mild solutions for nonlinear nonlocal impulsive evolution equation is obtained by using the perturbation method and the monotone iterative technique. The theorems proved in this paper improve and extend some related results in ordinary differential equations and partial differential equations. Moreover, we present two examples to illustrate the feasibility of our abstract results.
MSC:
93B40 | Computational methods in systems theory (MSC2010) |
93C73 | Perturbations in control/observation systems |
93C25 | Control/observation systems in abstract spaces |
93C15 | Control/observation systems governed by ordinary differential equations |
93C10 | Nonlinear systems in control theory |