摘要
利用锥上的Krasnosel’skii不动点定理考察了非线性项含有隅角和弯矩的四阶弹性梁方程的正解．在材料力学中,该方程描述了一类两端简单支撑的弹性梁的形变．结论表明这个方程可以具有n个正解,只要非线性项在某些有界集上的“高度”是适当的,其中n是一个任意的自然数．
By using the Krasnosel＇skii fixed point theorem on cone, the positive solutions are considered for the fourth-order elastic beam equation with corner and bending moment {u^（4）（t）=f（t,u（t）,u′（t））,0≤t≤1, u（0）=u（1）=u″（0）=u″（1）=0 In the material mechanics, the equation describes the deformation of an elastic beam whose both ends are simply supported. Our results show that the equation may have n positive solutions provided the ＂heights＂ of nonlinear term are appropriate on some bounded sets, where n is an arbitrary natural number.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
2006年第4期127-130,共4页
Journal of Lanzhou University(Natural Sciences)
关键词
非线性弹性梁方程
边值问题
正解
存在性
多解性
nonlinear elastic beam equation
boundary value problem
positive solution
existence
multiplicity
