A generalization of Guo's theorem and applications
type: Item
instance of: scholarly article
title: A generalization of Guo's theorem and applications
zbMATH Open document ID: 0632.47044
DOI: 10.1016/0022-247X(87)90063-1
author: Jingxian Sun
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The article [\textit{D. Guo}, Chin. Ann. Math. 2, Special Issue, 65-80 (1981; Zbl 0497.47032)] contains the following theorem: Let D be a bounded open set in infinite dimensional Banach space X and A: \(\bar D\to X\) be completely continuous. Suppose that (i) \(\inf_{x\in \partial D}\| Ax\| >0\) and (ii) Ax\(\neq \mu x\) for \(x\in \partial D\), \(0<\mu \leq 1\). Then the Leray-Schauder degree \(\deg (I-A,D,0)=0.\) The article extends this theorem to the case when A is a strict-set- contraction mapping and gives some applications.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 4028235
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: strict-set-contraction mapping
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
cites work: Q3962048
cites work: Q3958998
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cites work: Remarks on the paper “boundary conditions for condensing mappings”
cites work: Q3951115
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description: scientific article; zbMATH DE number 4028235