A generalization of Guo's theorem and applications
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.
scientific article; zbMATH DE number 4028235
scientific article