Abstract: This paper studies the existence of multiple positive solutions for elastic beam equations simply supported at both ends with inhomogeneous boundary conditions{Y ⁽⁴⁾(x)=f(x,y), x∈(0,1),y(0)=0, y(1)=b, y″(0)=0, y″(1)=0,where f∈C(［0,1］×［0,∞),［0,∞)), b>0, and f(x,s) is a monotone increasing function with respect to s for a fixed x∈［0,1］. Under appropriate conditions, there exists b^*>0 such that the problem has at least two positive solutions for 0*, at least one positive solution for b=b^*, and no positive solution for b>b^*. The proof of the main results is based on the upper and lower solution method and topological degree theory.

Key words: inhomogeneous, simple support, upper and lower solution, topological degree