Stepanov-Like Pseudo-Almost Periodicity and Semilinear Differential Equations with Uniform Continuity |
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Authors: | Hong-Xu Li Li-Li Zhang |
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Institution: | 1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People??s Republic of China
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Abstract: | By using the method of the invariant subspaces for unbounded linear operators and Schauder??s fixed point theorem, we give an existence theorem of mild pseudo-almost periodic solutions for some semilinear differential equations with a Stepanov-like pseudo-almost periodic term under some suitable assumptions. For this purpose, we show a new composition theorem of Stepanov-like pseudo-almost periodic functions. As applications, we examine the existence of mild pseudo-almost periodic solutions to some second-order hyperbolic equations. Our work is done under a ??uniform continuity?? condition instead of the ??Lipschitz?? condition assumed in the literature. |
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