Abstract
We investigate semilinear evolution equations of the form for and in Banach space . Under the assumptions that the evolution family has the exponential dichotomy and the function has the Carathéodory property, we show that the semilinear evolution equations on the line has a unique admissible solution, bounded solution, periodic solution when the function satisfies the condition -Lipschitz and there exists a periodic solution when the function satisfies the condition for all and almost everywhere .
Citation
Trinh Viet Duoc. "Admissible, bounded and periodic solutions of semilinear evolution equations on the line." J. Integral Equations Applications 34 (2) 183 - 199, Summer 2022. https://doi.org/10.1216/jie.2022.34.183
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