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ASYMPTOTICALLY $(\omega, c)$-ALMOST PERIODIC SOLUTIONS TO DIFFERENTIAL EQUATIONS IN BANACH SPACES
Keywords:
asymptotically $(\omega, c)$-almost periodic, $(\omega, c)$-almost periodic, composition theorem, semilinear differential equationDOI:
https://doi.org/10.17654/0972087124018Abstract
In this paper, we establish the existence and uniqueness result of asymptotically $(\omega, c)$-almost periodic mild solutions to semilinear differential equations in a Banach space. For this purpose, we first give some properties of $(\omega, c)$-almost periodic functions and asymptotically $(\omega, c)$-almost periodic functions, including the composition theorems. Then we obtain the existence and uniqueness result of $(\omega, c)$-almost periodic mild solution to the semilinear differential equation, and the existence and uniqueness theorems for $(\omega, c)$-almost periodic and asymptotically $(\omega, c)$-almost periodic mild solutions for the corresponding linear equation. Moreover, an example of the heat equation is given to illustrate the abstract results.
Received: July 6, 2024
Accepted: August 28, 2024
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