Stepanov-like pseudo-almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay |
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Authors: | Zhanrong Hu Zhen Jin |
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Institution: | aDepartment of Mathematics, North University of China, Taiyuan 030051, China;bSchool of Mechatronic Engineering, North University of China, Taiyuan 030051, China |
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Abstract: | In this paper, we prove the invariance of Stepanov-like pseudo-almost periodic functions under bounded linear operators. Furthermore, we obtain existence and uniqueness theorems of pseudo-almost periodic mild solutions to evolution equations u′(t)=A(t)u(t)+h(t) and on , assuming that A(t) satisfy “Acquistapace–Terreni” conditions, that the evolution family generated by A(t) has exponential dichotomy, that R(λ0,A()) is almost periodic, that B,C(t,s)t≥s are bounded linear operators, that f is Lipschitz with respect to the second argument uniformly in the first argument and that h, f, F are Stepanov-like pseudo-almost periodic for p>1 and continuous. To illustrate our abstract result, a concrete example is given. |
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Keywords: | Pseudo-almost periodic Stepanov-like pseudo-almost periodic Infinite delay Perturbed nonautonomous evolution equations Exponential dichotomy |
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