Abstract
This work aims to investigate the existence and uniqueness of pseudo almost automorphic solutions to semilinear differential equations in Banach space. By generalizing the Bihari type inequality and using Krasnoselski–Schaefer fixed point theorem, the existence results are deduced. Moreover, a new estimate is also built to ensure the existence and uniqueness of solutions. An example is given to illustrate our conclusions.
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J.-C. Chang: This research is supported in part by the National Science Council, Taipei, R. O. C. [NSC 101-2115-M-214-001].
D.-C. Luor: This research is supported in part by the Ministry of Science and Technology, R. O. C. [MOST 103-2632-M-214-001-MY3].
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Chang, JC., Luor, DC. Integral Inequalities and Pseudo Almost Automorphic Solutions to Semilinear Differential Equations in Banach Spaces. Mediterr. J. Math. 13, 4353–4368 (2016). https://doi.org/10.1007/s00009-016-0749-x
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DOI: https://doi.org/10.1007/s00009-016-0749-x