Abstract: By using the fixed point theorem on the cone, the author study a class of  cantilever beam equations{w″″(t)=λf(t,w(t)), t∈(0,1), w(0)=w′(0)=w″(1)=w(1)=0, where λ is a positive parameter, f∈C(［0,1］×［0,∞),［0,∞)). The existence and multiplicity results of its positive solutions are given when the nonlinear term f satisfies superlinear or sublinear growth condition.

Key words: cantilever beam equation, existence, multiplicity, positive solution, cone