Critical type of Krasnosel’skii fixed point theorem
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- by Tian Xiang and Rong Yuan
- Proc. Amer. Math. Soc. 139 (2011), 1033-1044
- DOI: https://doi.org/10.1090/S0002-9939-2010-10517-8
- Published electronically: August 2, 2010
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Abstract:
In this paper, by means of the technique of measures of noncompactness, we establish a generalized form of the fixed point theorem for the sum of $T+S$, where $S$ is noncompact, $I-T$ may not be injective, and $T$ is not necessarily continuous. The obtained results unify and significantly extend a number of previously known generalizations of the Krasnosel’skii fixed point theorem. The analysis presented here reveals the essential characteristics of the Krasnosel’skii type fixed point theorem in strong topology setups. Further, the results are used to prove the existence of periodic solutions of a nonlinear neutral differential equation with delay in the critical case.References
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Bibliographic Information
- Tian Xiang
- Affiliation: Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Ministry of Education, Beijing 100875, People’s Republic of China
- Email: tianx@mail.bnu.edu.cn
- Rong Yuan
- Affiliation: Laboratory of Mathematics and Complex Systems, School of Mathematical Sciences, Beijing Normal University, Ministry of Education, Beijing 100875, People’s Republic of China
- Email: ryuan@bnu.edu.cn
- Received by editor(s): March 14, 2009
- Received by editor(s) in revised form: March 29, 2010
- Published electronically: August 2, 2010
- Additional Notes: This work was supported by National Natural Science Foundation of China
- Communicated by: Yingfei Yi
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1033-1044
- MSC (2010): Primary 47H08, 47H10, 37C25
- DOI: https://doi.org/10.1090/S0002-9939-2010-10517-8
- MathSciNet review: 2745654