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Fixed points of decreasing operators in ordered Banach spaces and applications to nonlinear second order elliptic equations. (English) Zbl 1191.47075
Summary: We consider some decreasing operators in ordered Banach spaces. We study the existence and uniqueness of fixed points and properties of the iterative sequences for these operators. Lastly, the results are applied to nonlinear second order elliptic equations.

MSC:
47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47N20 Applications of operator theory to differential and integral equations
35J61 Semilinear elliptic equations
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