Abstract: By using the methods of upper and lower solutions  and topological degree theory, the author discusses the existence and multiplicity of positive solutions for the nonlinear simply supported static beam equations  with a parameter. where λ>0 is a parameter, k₁<k₂<0, k₁ and k₂ are real constants, f: ［0,1］×［0,∞)→(0,∞) is a continuous function, and f(x,y)  monotonically increases with respect to y for a fixed x∈［0,1］.

Key words: positive solution, existence, multiplicity, upper and lower solutions, topological degree