时滞中立型发展方程的周期解
Periodic solutions for neutral evolution equations with delays
摘要：
研究Banach空间$X$中中立型发展方程$$(u(t)-G(t,u(t-ξ)))'+Au(t)=F(t,u(t),u(t-τ)),\ \ \ \ t\in\R$$的周期解问题，其中$A:D(A)\subset X\rightarrow X$是闭线性算子，$-A$生成一个紧解析算子半群$T(t)(t\geq0)$ .利用解析算子半群理论和一些不动点定理，得到了中立型发展方程周期温和解的存在唯一性。研究了时滞发展方程周期温和解的正则性，得到了经典解和强解的存在性结果.最后，我们给出了一个例子来说明抽象结果的适用性。我们的工作改进和推广了已有文献的相关结果。
英文摘要：
The aim is to study the periodic solution problem for neutral evolution equation $$(u(t)-G(t,u(t-ξ)))'+Au(t)=F(t,u(t),u(t-τ)),\ \ \ \ t\in\R$$in Banach space $X$, where $A:D(A)\subset X\rightarrow X$ is a closed linear operator, and $-A$ generates a compact analytic operator semigroup $T(t)(t\geq0)$. With the aid of the analytic operator semigroup theories and some fixed point theorems, we obtain the existence and uniqueness of periodic mild solution for neutral evolution equations. The regularity of periodic mild solution for evolution equation with delay is studied, and some the existence results of the classical and strong solutions are obtained. In the end, we give an example to illustrate the applicability of abstract results. Our works greatly improve and generalize the relevant results of existing literatures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
