A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations |
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Authors: | Chengbo Zhai Douglas R. Anderson |
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Affiliation: | a School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, PR China b Department of Mathematics and Computer Science, Concordia College, Moorhead, MN 56562, USA |
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Abstract: | This paper is concerned with an operator equation Ax+Bx+Cx=x on ordered Banach spaces, where A is an increasing α-concave operator, B is an increasing sub-homogeneous operator and C is a homogeneous operator. The existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators. As applications, we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth-order two-point boundary value problems for elastic beam equations and elliptic value problems for Lane-Emden-Fowler equations. |
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Keywords: | Positive solution Operator equation Normal cone Fixed point Elastic beam equation Lane-Emden-Fowler equation |
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