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

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.