Weighted pseudo almost automorphic solutions to nonautonomous semilinear evolution equations with delay and $S^{p}$-weighted pseudo almost automorphic coefficients
Keywords
Stepanov-like weighted pseudo almost automorphic, nonautonomous semilinear evolution equations, delayAbstract
By some new properties of Stepanov-like weighted pseudo almost automorphic functions established by Chang, Zhang and N'Guérékata recently, we shall deal with weighted pseudo almost automorphic solutions to the nonautonomous semilinear evolution equations with a constant delay: $u'(t)=A(t)u(t)+f(t,u(t-h))$, $ t\in\mathbb{R}$ in a Banach space $\mathbb{X}$, where $A(t),t\in\mathbb{R}$ generates an exponentially stable evolution family $\{U(t,s)\}$ and $f \colon\mathbb{R}\times\mathbb{X} \rightarrow \mathbb{X}$ is a $\S^{p}$-weighted pseudo almost automorphic function satisfying some suitable conditions. We obtain our main results by the Leray-Shauder Alternative theorem.Downloads
Published
2016-04-12
How to Cite
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CHANG, Yong-Kui, ZHANG, Rui and N’GUÉRÉKATA, G. M. Weighted pseudo almost automorphic solutions to nonautonomous semilinear evolution equations with delay and $S^{p}$-weighted pseudo almost automorphic coefficients. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 43, no. 1, pp. 69 - 88. [Accessed 21 May 2024].
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