An Existence Result of Positive Solutions for the Bending Elastic Beam Equations

This paper is concerned with the existence of positive solutions to fourth-order boundary value problem u(4)(x)=f(x,u(x),u″(x)) on interval [0, 1] condition u(0)=u(1)=u″(0)=u″(1)=0, which models a statically bending elastic beam whose two ends are simply supported. Without assuming that nonlinearity f(x, u, v) nonnegative, an result obtained under inequality conditions |(u, v)| small or large enough. The discussion based method lower and upper solutions.