Topological Methods in Nonlinear Analysis

Weighted pseudo almost automorphic solutions to nonautonomous semilinear evolution equations with delay and ${\rm S}^{p}$-weighted pseudo almost automorphic coefficients

Yong-Kui Chang, Rui Zhang, and G. M. N'Guérékata

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 43, Number 1 (2014), 69-88.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381548

Mathematical Reviews number (MathSciNet)
MR3236600

Zentralblatt MATH identifier
1365.34131

Citation

Chang, Yong-Kui; Zhang, Rui; N'Guérékata, G. M. 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 (2014), no. 1, 69--88. https://projecteuclid.org/euclid.tmna/1460381548


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