一类二阶常微分方程多重正解的存在性

由于物理学和力学中的许多问题最终可以归结为一类二阶常微分方程的边值问题，此类问题的解的存在性和多重性得到了许多学者的研究．通过将常微分方程转化为非线性积分方程，利用锥拉伸和锥压缩不动点定理和不动点指数讨论了一类二阶常微分方程的正解存在性问题，在一定条件下，得到了几个多重正解定理，同时证明了与此相关的主要引理．

Multiple Positive Solutions Theorem of a Class of the Second Order Differential Equations Problems

Owing to the importance of a class of second order differential equations problems in physics and mechanics,the existence and multiplicity of the solutions to those problems have been studied by many scholars.By changing differential equations into nonlinear integral equation,we study the existence of positive solution of a class of second order differential equations problems by the fixed point theorem of cone expansion and compression,and the fixed point index theorem,then we obtain two multiple positive solutions theorems under some conditions,and give the proof of main lemmas that are important to our discussion.