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Fixed point theorems for mixed monotone operators with PPF dependence. (English) Zbl 1162.47042
First, the authors prove an existence result for coupled fixed points of mixed monotone operators. The uniqueness of such fixed points is also proved, but just in a region of the domain of the involved operator. In the last section, the authors use this result as well as one of their previous results to prove the existence and uniqueness for the solution of a PVBP with delay, in the minimal class.
MSC:
47H10Fixed point theorems for nonlinear operators on topological linear spaces
34B15Nonlinear boundary value problems for ODE
47H05Monotone operators (with respect to duality) and generalizations
47N20Applications of operator theory to differential and integral equations