Abstract
In this paper, we concern on the periodic boundary value problem for a class of semilinear impulsive fractional evolution equations in an ordered Banach space E. First, we establish the existence results of mild solutions for the associated linear periodic boundary value problem. Next, we obtain the existence results of mild solutions by using the monotone iterative technique with L-quasi-upper and lower solutions, the results are new and extend some previously known results. Finally, two examples are also given to illustrate the main results.
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The authors would like to thank the referees for their useful suggestions which have significantly improved the paper.
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This work is supported by the National Natural Science Foundation of China (Grant No. 11661071).
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Gou, H., Li, Y. Existence of mild solutions for impulsive fractional evolution equations with periodic boundary conditions. J. Pseudo-Differ. Oper. Appl. 11, 425–445 (2020). https://doi.org/10.1007/s11868-019-00278-2
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DOI: https://doi.org/10.1007/s11868-019-00278-2
Keywords
- Monotone iterative technique
- Coupled L-quasi-upper and lower solutions
- Periodic boundary conditions
- Analytic semigroup