<p style='text-indent:20px;'>This paper is mainly concerned with the existence of pseudo <i>S</i>-asymptotically Bloch type periodic solutions to damped evolution equations in Banach spaces. Some existence results for classical Cauchy conditions and nonlocal Cauchy conditions are established through properties of pseudo <i>S</i>-asymptotically Bloch type periodic functions and regularized families. The obtained results show that for each pseudo <i>S</i>-asymptotically Bloch type periodic input forcing disturbance, the output mild solutions to reference equations remain pseudo <i>S</i>-asymptotically Bloch type periodic.</p>

中文翻译：

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阻尼演化方程的伪$S$-渐近布洛赫型周期解

<p style='text-indent:20px;'>本文主要研究Banach空间阻尼演化方程的伪<i>S</i>-渐近Bloch型周期解的存在性。通过伪<i>S</i>-渐近Bloch型周期函数和正则化族的性质，建立了经典Cauchy条件和非局部Cauchy条件的一些存在性结果。所得结果表明，对于每个伪<i>S</i>-渐近Bloch型周期输入强迫扰动，参考方程的输出温和解保持伪<i>S</i>-渐近Bloch型周期。</ p>