一类四阶边值问题的分析

数学物理学报 ›› 2005, Vol. 25 ›› Issue (6): 890-897.

一类四阶边值问题的分析

李晓聪, 江成顺

信息工程大学信息工程学院郑州 |450002

出版日期:2005-12-24 发布日期:2005-12-24
基金资助:
河南省高校杰出科研人才创新工程基金（2003KJCX008）资助

Analysis for Some Fourth Order Boundary Value Problems

LI Xiao-Cong, JIANG Cheng-Shun

Online:2005-12-24 Published:2005-12-24
Supported by:
河南省高校杰出科研人才创新工程基金（2003KJCX008）资助

摘要/Abstract

摘要：

该文考虑的四阶边值问题，可用于描述飞机、轮船及建筑物的结构模型。由经典的分析方法，如辅助的截断函数，Schauder不动点定理，作者首先提出一种改进的上、下解方法；然后，利用二阶齐次边值问题的第一特征函数，构造出具体的上解，同时取0为相应下解，在更一般的假设下得到正解的存在性；
最后探讨了右端项f(x,y,z)在y=0奇异的情形。

关键词: 上、下解;Schauder不动点定理;奇异

Abstract:

This paper is concerned with a class of fourth\|order boundary value problems. By some classical analysis methods, such as, defining an auxiliary truncation function, and Schauder fixed point theory, the authors develop the method of upper and lower solutions. Secondly, with the first eigenfunction of homogeneous boundary value problems, they construct a specific upper solution, and at the same time, 0 is taken as the corresponding lower one, thus the existence theorem of positive solutions is proved under more general assumptions. The case, when f(x,y,z) is singular at y=0 is discussed in the end.

Key words: Upper and lower solutions, Schauder fixed point the orem, Singular

中图分类号:

35B05

李晓聪, 江成顺. 一类四阶边值问题的分析[J]. 数学物理学报, 2005, 25(6): 890-897.

LI Xiao-Cong, JIANG Cheng-Shun. Analysis for Some Fourth Order Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2005, 25(6): 890-897.

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