A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:375

Article

Zhai, Chengbo¹  Anderson, Douglas R.² 

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

[2] Concordia Coll, Dept Math & Comp Sci, Moorhead, MN 56562 USA

关键词: Positive solution;    Operator equation;    Normal cone;    Fixed point;    Elastic beam equation;    Lane-Emden-Fowler equation;   

DOI  :  10.1016/j.jmaa.2010.09.017

来源: Elsevier

【 摘 要 】

This paper is concerned with an operator equation Ax + Bx + Cx = x on ordered Banach spaces, where A is an increasing alpha-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 beta-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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free