一类四阶两点边值问题多个正解的存在性  

Existence of Multiple Positive Solutions for a Class of Fourth-order Two-point Boundary Value Problems

作　　者：闫东明[1] 

机构地区：[1]西北师范大学数学与信息科学学院,兰州730070

出　　处：《工程数学学报》2010年第1期133-138,共6页Chinese Journal of Engineering Mathematics

基　　金：高等学校博士学科点专项科研基金(20060736001)~~

摘　　要：两端简单支撑弹性梁的形变可以用四阶常微分方程两点边值问题来描述。由于其在物理中的重要性,已有许多人研究了该类问题解的存在性,但在实际应用中该类问题正解以及多个正解的存在性更为重要。本文应用锥上的不动点定理,研究了该类四阶常微分方程两点边值问题多个正解的存在性,给出了该类问题多个正解存在的充分条件,本文结果推广和改进了一些已知结果。最后给出一例作为所获结果的应用。The deformations of an elastic beam in equilibrium state, whose two ends are simply supported, can be described by a fourth-order ordinary differential equation boundary value problem. Owing to its importance in physics, the existence of solutions to this problem has been studied by many authors. But in practice, only its positive solution is significant. The existence of multiple positive solutions for some fourth-order two-point boundary value problems are obtained by using the fixed point theorem in cone. The obtained results improve and extend the existing results partially. In the end, an example is presented to illustrate the application of the obtained results.

关 键 词：四阶边值问题 锥 多个正解 存在性 

分 类 号：O175.8[理学—数学]