一个非线性四阶梁方程三解定理的新证明

A New Proof of Three Solutions for a Nonlinear Fourth-order Beam Equation

应用Morse理论,给出了四阶梁方程{u(4)=f(t,u(t)),t∈[0,1] u(0)=u(1)=u″(0)=u″(1)=0三解存在性的一个新证明,其中f∈C1([0,1]×R1,R1).

In this paper, a new proof of existence theorem on three solutions for the following fourth - order beam equation is obtained ：{u（4）=f（t,u（t））,t∈[0,1] u（0）=u（1）=u″（0）=u″（1）=0,where,f∈C1（[0,1]×R1,R1）.The Morse theorem is applied to discuss thisproblem.