摘要
在工程实际中,四阶两点边值问题u(4)=f(t,u(t)),t∈[0,1]用来描述弹性梁在垂直轴线外力作用下的形变.一端为固定铰支,一端为可动铰支的梁称为简支梁,它在两端点的位移与弯矩均为零,故其相应的边界条件为u(0)=u(1)=u(0)=u(1)=0.本文应用下降流不变集方法研究了一类简支梁方程,在非线性项f在0处渐近线性、∞处超二次的条件下,证明了方程存在一个正解.主要结果及其证明方法均不同于文献中的结果.
In engineering, the fourth-order two-point boundary value problem u^(4) f(t,u(t)), t ∈[0, 1] is used to describe the deformation of an elastic beam un- der external vertical forces. A beam that has hinged connection at one end and roller connection in other end is called simply supported beam, and its correspond- ing equation satisfies the boundary condition u(0) = u(1) = u"(0) = u"(1) = 0 since its displacements and bending moments at both ends are equal to zero. In the paper, by using the descending flow invariant set method, it is proved that there exists a positive solution for a class of simply supported beam equations under the assumption that the nonlinear term f is asymptotically linear at 0 and superquadric at ∞ in u. The main result and its proof are quite different from those presented by other literature.
出处
《工程数学学报》
CSCD
北大核心
2013年第3期467-474,共8页
Chinese Journal of Engineering Mathematics
基金
The National Natural Science Foundation of China(11101253
10826081
10871123)
the Fundamental Research Funds for the Central Universities(GK200902046)
the Scientific Research Foundation of Xi’an University of Science and Technology(200843)
关键词
四阶边值问题
正解
非线性算子
临界点
fourth-order boundary value problems
positive solution
nonlinear operator
critical point