四阶非局部边值问题的正解的存在性

J4 ›› 2010, Vol. 45 ›› Issue (12): 62-66.

四阶非局部边值问题的正解的存在性

孙涛¹,高飞¹,段晓东²

1.东北大学理学院, 辽宁沈阳 110004; 2.大连民族学院计算机学院, 辽宁大连 116600

收稿日期:2009-05-26 出版日期:2010-12-16 发布日期:2011-03-16
作者简介:孙涛(1959-),男,硕士,副教授,研究方向为非线性泛函分析.Email:suntao988254@sina.com
基金资助:
国家自然科学基金资助项目(60573124)

The existence of positive solutions of nonlocal boundary value problems for the fourth order

SUN Tao¹, GAO Fei¹, DUAN Xiao-dong²

1. Department of Mathematics, Northeastern University, Shenyang 110004, Liaoning, China;
2. School of Computer, Dalian Nationalities University, Dalian 116600, Liaoning, China

Received:2009-05-26 Online:2010-12-16 Published:2011-03-16

摘要/Abstract

摘要：

应用锥拉伸与锥压缩不动点定理,讨论了一类非线性四阶微分方程非局部边值问题的正解的存在性,构造了一个合适的锥和凸泛函,得到了该问题正解的存在性。

关键词: 非局部边值问题;正解;锥拉伸与锥压缩;凸泛函;锥

Abstract:

The nonlocal boundary value problem for a nonlinear fourth-order ordinary differential equation is considered. The existence of positive soluations is shown to the problem above by applying a generalization of the cone expansion and compression fixed point theorem. In order to study this problem, cone and convex functional are introduced. This method is different from others which discussed the existence of positive solutions about the problem.

Key words: nonlocal boundary value problems; positive solutions; cone expansion compression; convex functional; cone

孙涛1,高飞1,段晓东2. 四阶非局部边值问题的正解的存在性[J]. J4, 2010, 45(12): 62-66.

SUN Tao1, GAO Fei1, DUAN Xiao-dong2. The existence of positive solutions of nonlocal boundary value problems for the fourth order[J]. J4, 2010, 45(12): 62-66.

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