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Nonlocal Cauchy problems governed by compact operator families

Affiliation:	1. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;2. College of Science, Guizhou Institute of Technology, Guiyang, Guizhou 550025, PR China;3. Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, PR China;4. Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China;5. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

Abstract:	We study the existence of mild solutions for the nonlocal Cauchy problem $u′(t)=Au(t)+f(t,u(t)), t∈[t_{0},t_{0} +T], u(t_{0})+g(u)=u_{0},$ and give new criterions, which extend some existing results in this area.

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