一类弯曲的弹性梁方程正解的存在性  

Existence of Positive Solutions for a Bending Elastic Beam Equation

作　　者：霍会霞 李永祥 Huo Huixia;Li Yongxiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学物理学报（A辑）》2024年第6期1476-1484,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(12061062,12161080)

摘　　要：该文讨论四阶常微分方程边值问题{u(4)(x)=f(x,u(x),u′′(x)),x∈[0,1],u′(0)=u′′′(0)=u(1)=u′′(1)=0正解的存在性,其中,f:[0,1]×R+×R−→R+连续,该问题是描述一类弹性梁静态形变的数学模型.在非线性项f(x,u,v)满足适当的不等式条件下,应用锥上的不动点指数理论获得了正解的存在性结果.This paper discusses the existence of the positive solution of the fourth-order boundary value problem{u(4)(x)=f(x,u(x),u′′(x)),x∈[0,1],u′(0)=u′′′(0)=u(1)=u′′(1)=0,which models the deformations of a statically elastic beam,where f:[0,1]×R+×R−→R+is continuous.Under that the nonlinearity f(x,u,v)satisfies some inequality conditions,the existence results of positive solutions of this problem are obtained by applying the fixed point index theory in cones.

关 键 词：四阶边值问题 正解 锥 不动点指数 

分 类 号：O175.8[理学—数学]