一类非线性弹性梁方程的正周期解  

Positive Periodic Solutions of a Class of Nonlinear Elastic Beam Equations

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,江苏南京210003

出　　处：《河北大学学报（自然科学版）》2009年第3期225-228,共4页Journal of Hebei University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571085)

摘　　要：利用锥上的不动点指数定理考察了一类非线性弹性梁方程的正周期解的局部存在性.这类方程没有Green函数,通过适当的变换克服了这个困难.主要结论表明该类方程能够具有n个正解,只要非线性项在某些有界集合上的最大值和最小值都是适当的.The local existence of positive periodic solutions is considered for a class of nonlinear elastic beam equations by applying the index theorem of fixed point on cone. This class of equations has not Green function. The difficulty is surmounted by a suitable transformation. The main results show that the class of equations can have n positive solutions provided the maximum and minimum of nonlinear term on some bounded sets are appropriate.

关 键 词：周期边值问题 正解 存在性 多解性 

分 类 号：O175.8[理学—数学]