Existence and uniqueness of positive mild solutions for nonlocal evolution equations

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• 作者：Pengyu Chen ; Yongxiang Li ; Xuping Zhang
• 关键词：Abstract evolution equation ; Nonlocal initial condition ; Positive $$C_0$$ C 0 ; semigroup ; Existence and uniqueness ; Spectral radius ; 34G20 ; 34K30 ; 35D35 ; 47D06
• 刊名：Positivity
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：19
• 期：4
• 页码：927-939
• 全文大小：450 KB
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• 作者单位：Pengyu Chen (1)
  Yongxiang Li (1)
  Xuping Zhang (1) (2)
  
  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People鈥檚 Republic of China
  2. Department of Mathematics, Zhixing College of Northwest Normal University, Lanzhou, 730070, People鈥檚 Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Operator Theory
  Potential Theory
  Calculus of Variations and Optimal Control
  Econometrics
  
• 出版者：Birkh盲user Basel
• ISSN：1572-9281

文摘

This paper deals with the existence and uniqueness of positive mild solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The existence and uniqueness of mild solution for the associated linear evolution equation nonlocal problem is established, and the spectral radius of resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness of positive mild solutions for nonlinear evolution equation nonlocal problem are obtained by using the monotone iterative method without the assumption of lower and upper solutions. The theorems proved in this paper improve and extend some related results in ordinary differential equations and partial differential equations. An example is also given to illustrate that our results are valuable. Keywords Abstract evolution equation Nonlocal initial condition Positive \(C_0\)-semigroup Existence and uniqueness Spectral radius