Structure of solution sets to the nonlocal problems

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• 作者：Yi Cheng ; Ben Niu ; Cuiying Li
• 关键词：34B15 ; 34B16 ; 37J40 ; evolution inclusions ; nonlocal conditions ; compact R δ $R_{\delta}$ ; path connected
• 刊名：Boundary Value Problems
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,566 KB
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• 作者单位：Yi Cheng (1)
  Ben Niu (1)
  Cuiying Li (2)
  
  1. Department of Mathematics, Bohai University, Jinzhou, 121012, P.R. China
  2. The Center of Teaching Reform and Evaluation, Bohai University, Jinzhou, 121012, P.R. China
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

This paper deals with the structural properties of the solution set for a class of nonlinear evolution inclusions with nonlocal conditions. For the nonlocal problems with a convex-valued right-hand side it is proved that the solution set is compact \(R_{\delta}\); it is the intersection of a decreasing sequence of nonempty compact absolute retracts. Then for the cases of a nonconvex-valued perturbation term it is proved that the solution set is path connected. Finally some examples of nonlinear parabolic problems are given. Keywords evolution inclusions nonlocal conditions compact \(R_{\delta}\) path connected