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Four functionals fixed point theorem. (English) Zbl 1187.34035
Summary: The four functionals fixed point theorem is a generalization of the original, as well as the functional generalizations, of the Leggett-Williams fixed point theorem. In the four functionals fixed point theorem, neither the upper nor the lower boundary of the underlying set is required to map below or above the boundary in the functional sense. As an application, the existence of a positive solution to a second-order right focal boundary value problem is considered by applying both standard and nonstandard choices of functionals. An extension to multivalued maps is provided for completeness.
34B18Positive solutions of nonlinear boundary value problems for ODE
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N20Applications of operator theory to differential and integral equations
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