Fixed points of decreasing operators in ordered Banach spaces and applications to nonlinear second order elliptic equations☆

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Abstract

In this paper, 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.

Keywords

Ordered Banach space
Decreasing operator
Fixed point
Iterative sequence

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Research supported by the National Natural Science Foundation of China (10871116), the Natural Science Foundation of Shandong Province of China (Y2006A04) and the Doctoral Program Foundation of Education Ministry of China (200804460001).

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