A necessary and sufficient condition for the existence of symmetric positive solutions of higher-order boundary value problems

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Abstract

A necessary and sufficient condition is obtained for the existence of symmetric positive solutions to higher-order nonlinear boundary value problems. The uniqueness, an iterative sequence and an error estimation for symmetric positive solutions are also discussed. Moreover, we give an example to illustrate the applicability of our results. Our analysis mainly relies on the monotone iterative technique.

Keywords

Higher-order boundary value problems
Symmetric positive solutions
Existence
Monotone iterative technique
Necessary and sufficient condition

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Supported by the National Natural Sciences Foundation of China (10871063) and Scientific Research Fund of Hunan Provincial Education Department (07A038).