Perturbation method for nonlocal impulsive evolution equations |
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| Institution: | 1. School of Control Science and Engineering, Shandong University, Jiman 250061, PR China;2. Key Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;1. School of Mathematical Sciences, Ocean University of China, Qingdao, China;2. Faculty of Management, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada;3. Department of Operations Research and Information Engineering, Beijing University of Technology, Beijing, China;1. Department of Economics, School of Economics and Management, Beijing Jiaotong University, Beijing, 100044, China;2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China;3. University of Chinese Academy of Sciences, Beijing, 100049, China |
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| Abstract: | 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 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 perturbation method and 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. |
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