Abstract
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 ${\rm S}^{p}$-weighted pseudo almost automorphic function satisfying some suitable conditions. We obtain our main results by the Leray-Shauder Alternative theorem.
Citation
Yong-Kui Chang. Rui Zhang. G. M. N'Guérékata. "Weighted pseudo almost automorphic solutions to nonautonomous semilinear evolution equations with delay and ${\rm S}^{p}$-weighted pseudo almost automorphic coefficients." Topol. Methods Nonlinear Anal. 43 (1) 69 - 88, 2014.
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