The problem U(4) (t) = f (t ,U) , t ∈ (o, 1) with the boundary value conditions u″ (0) = u″ (1) = O ,u (O)=u(l) =O is studied by using topological degree and Morse theory. Under some conditions, we obtain this problem has at least six solutions,including two positive solutions, two negative solutions and two sign-changing solutions.%利用拓扑度理论和Morse理论研究方程u(4)(t)=f(t,u),t∈(0,1),且带有边界条件u"(0)=u"(1)=0,u(0)=u(1)=0.在一定条件下,得到此问题有六个解,其中两个正解,两个负解,两个变号解.
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