Existence of pseudo-almost automorphic solutions for nonlinear differential equations |
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| Authors: | Lan Li Yan Wang |
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| Institution: | 1. College of Mathematics and Computational Science, Shenzhen University, Shenzhen, 518060, China
2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
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| Abstract: | In this paper, we discuss the existence of pseudo-almost automorphic solutions to linear differential equation which has an exponential trichotomy, and the results also hold for some nonlinear equations with the form x′(t) = f(t, x(t)) + λ g (t, x(t)), where f, g are pseudo-almost automorphic functions. We prove our main result by the application of Leray-Schauder fixed point theorem. |
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| Keywords: | Pseudo-almost automorphic exponential trichotomy Leray-Schauder fixed point theorem |
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