On the homotopy property of topological degree for maximal monotone mappings
Section snippets
Introduction and preliminaries
Topological degree theory is a very powerful tool used in proving various existence results for nonlinear partial differential equations and it has received a lot of attention in the literature, see the references in [17]. In 1983, Browder established a degree theory for single valued mappings of class , (see also [18] for the separable space case). Based on this degree, Browder also constructed a degree theory for mappings of class with a perturbation of a maximal monotone mapping or
Main results
In the following, E is a real reflexive Banach spaces, the dual space of E, and both E and are locally uniform convex spaces. Theorem 2.1 Let , be two maximal monotone mappings. Let be an open bounded subset, and . Assume that , and , , and . Then . Proof For any , we claim that there exists such thatSuppose this is not true. There
Acknowledgement
The first author was supported by a NSFC grant, Grant No. 10871052.
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