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Leggett–Williams theorems for coincidences of multivalued operators. (English) Zbl 1152.47041
Let X,Y be Banach spaces, C be a cone in X and let Ω 1 ,Ω 2 be open bounded subsets of X with Ω ¯ 1 Ω 2 . For a pair (L,N) consisting of a linear Fredholm operator L:domLXY of zero index and an upper semicontinuous (compact convex)-valued multimap N:XY, the authors study the existence of a coincidence point (LxNx) in C(Ω ¯ 2 Ω 1 ). They use topological degree methods under some compactness or condensivity conditions. As application, the existence of positive periodic solutions for a differential inclusion is considered.

MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
34A60Differential inclusions
34C25Periodic solutions of ODE
47H04Set-valued operators
47H11Degree theory (nonlinear operators)
54H25Fixed-point and coincidence theorems in topological spaces