【摘要】 文章讨论了Banach空间X中半线性时滞发展方程u′(t)+Au(t)=F(t,u(t),u(t-τ)),t∈Rω-周期解的存在性,其中-A为X中的C0-半群T(t)(t≥0)的无穷小生成元,F:R×X×X→X连续,关于t以ω为周期,τ>0为常数。通过对解算子的周期延拓,利用相关的不动点定理,获得了时滞发展方程ω-周期mild解的存在性结果。最后,给出了一个例子来说明主要结果的应用。文章不再要求先验有界和非线性项Lipschitz连续,这极大地改进和推广了现有文献的相关结果。更多还原

【Abstract】 We discuss the existence ofω-periodic solutions for the semilinear delay evolution equation u′(t)+Au(t)=F(t,u(t),u(t-τ)), t∈R in a Banach space X,where-Ais the infinitesimal generator of a C0-semigroup,and F:R×X×X→Xis a continuous mapping which isω-periodic in t,andτ>0 is a constant.With the aid of the periodic extension of the solution operator,the existence results of theω-periodic mild solutions are obtained by using the related fixed point theorems.Moreover,we present an example to illustrate the application of the main results.Moreover,the assumption of prior boundedness of solutions is not employed and there is no need to demand the nonlinear function satisfying Lipschitz continuous,which greatly improve and generalize the relevant results of existing literatures.更多还原