两端固接的奇异弹性梁方程正解的存在唯一性  

The Existence and Uniqueness of Positive Solutions to the Singular Elastic Beam Equation Rigidly Fixed at Both Ends

作　　者：杨东晖 

机构地区：[1]黑龙江东北煤炭矿山设备租赁公司,哈尔滨150001

出　　处：《工程数学学报》2009年第5期890-894,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571021)

摘　　要：利用锥上的混合单调算子不动点定理,本文研究了一类四阶奇异非线性微分方程的边值问题,即一类弹性梁方程问题。在力学上,该方程描述了两端固接的弹性梁的挠度。该文在非线性项是混合单调的条件下,得到了该方程正解的存在唯一性。作为主要结论的应用,我们给出了一个例子。By using a fixed point theorem of mixed monotone operators in cone,this paper studied a fourth-order nonlinear singular boundary value problem,namely a class of elastic beam equation. In mechanics,the equation describes the deffection of an elastic beam rigidly fixed at both ends. The existence and uniqueness of positive solutions are established for the elastic beam equation where the nonlinear term is mixed monotone. An example is presented to demonstrate the application of our main result.

关 键 词：边值问题 混合单调算子 不动点定理 弹性梁方程 唯一性 

分 类 号：O175.0[理学—数学]