New fixed point theorems for mixed monotone operators and local existence-uniqueness of positive solutions for nonlinear boundary value problems |
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Authors: | Chengbo Zhai Lingling Zhang |
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Institution: | a School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China b Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, PR China |
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Abstract: | In this article we present a new fixed point theorem for a class of general mixed monotone operators, which extends the existing corresponding results. Moreover, we establish some pleasant properties of nonlinear eigenvalue problems for mixed monotone operators. Based on them the local existence-uniqueness of positive solutions for nonlinear boundary value problems which include Neumann boundary value problems, three-point boundary value problems and elliptic boundary value problems for Lane-Emden-Fowler equations is proved. The theorems for nonlinear boundary value problems obtained here are very general. |
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Keywords: | Fixed point Mixed monotone operator Local existence-uniqueness Positive solution Nonlinear boundary value problem |
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