| 脉冲依赖状态的发展方程初值问题解的存在性 |
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| 引用本文： | 刘旭. 脉冲依赖状态的发展方程初值问题解的存在性[J]. 安徽大学学报(自然科学版), 2015, 0(4): 5-9. DOI: 10.3969/j.issn.1000-2162.2015.04.002 |
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| 作者姓名： | 刘旭 |
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| 作者单位： | 兰州交通大学数理学院,甘肃兰州,730070 |
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| 基金项目： | 国家自然科学基金资助项目(11261028);甘肃省科技计划基金资助项目 |
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| 摘 要： | 研究Rn中脉冲依赖状态的半线性发展方程初值问题u′(t)+Au(t)=f(t,u(t))a.e.t∈J=[0,a],t≠τk(u(t)),k=1,2,…,m;u(t+)=Ik(u(t)),t=τk(u(t)),k=1,2,…,m;u(0)=u0解的存在性.其中-A生成Rn的等度连续C0-算子半群的生成元.在f满足较弱的L1-Caratheodory条件下,逐段使用Schaefer不动点定理获得其mild解的存在性结果.
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| 关 键 词： | 发展方程 脉冲依赖状态 C0-半群 初值问题 |
Existence of solution of initial value problem for evolution equation with state-dependent impulses |
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| LIU Xu. Existence of solution of initial value problem for evolution equation with state-dependent impulses[J]. Journal of Anhui University(Natural Sciences), 2015, 0(4): 5-9. DOI: 10.3969/j.issn.1000-2162.2015.04.002 |
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| Authors: | LIU Xu |
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| Abstract: | T his paper discussed the existence to solutions of initial value problem for semilinear evolution equation with state‐dependent impulses u′(t)+ A u(t)= f (t ,u(t)) ,a .e . t∈ J= [0 ,a] ,t≠ τk (u(t)) ,k=1 ,2 ,… ,m;u(t+ )= Ik (u(t)) ,t= τk (u(t)) ,k= 1 ,2 ,… ,m;u(0)= u0 in space Rn ,where ‐A was the infinitesimal generator of an equicontinuous C0‐semigroup .In the case where f satisfied a weaker L1‐Caratheodory condition ,the Schaefer fixed‐point theorem was piecewise used to obtain the existence results of mild solution . |
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| Keywords: | evolution equation state-dependent impulses C0-semigroup initial value problem |
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