The objective of our research is to demonstrate the controllability of mild solutions for a specific class of second-order neutral functional evolution equations that involve state-dependent delay. To achieve this, we rely on Avramescu’s nonlinear alternative theorem and leverage cosine function theory.

中文翻译：

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具有状态相关时滞的二阶中性演化方程温和解的可控性

我们研究的目的是证明涉及状态相关延迟的特定类二阶中性函数演化方程的温和解的可控性。为了实现这一目标，我们依靠 Avramescu 的非线性替代定理并利用余弦函数理论。