一类梁方程的正解(英文)  

Positive Solutions for a Class of Beam Equations

作　　者：武瑛[1] 韩国栋[2] 

机构地区：[1]西安科技大学理学院,西安710054 [2]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》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)

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.

关 键 词：四阶边值问题 正解 非线性算子 临界点 

分 类 号：O175.8[理学—数学]