Picard and weakly Picard operators technique for nonlinear differential equations in Banach spaces |
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| Authors: | JinRong Wang Yong Zhou Milan Medved̆ |
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| Affiliation: | 1. Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, PR China;2. Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, PR China;3. Department of Mathematical and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia |
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| Abstract: | In this paper we study nonlocal Cauchy problems for differential equations in Banach spaces. Using Picard and weakly Picard operators technique and suitable Bielecki norms, some existence, uniqueness and data dependence results are obtained under some mild conditions. As an application, we also discuss a class of impulsive Cauchy problems by adapting the same methods. |
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