Positive Solutions of a Nonlinear Fourth-Order Boundary Value Problem with a Simply Supported End and a Movable End

By applying a Green function of third-order two-point boundary value problem and the Krasnosel'skii fixed point theorem of cone expansion-compression type,the existence and multiplicity of positive solutions is studied for a nonlinear fourth-order boundary value problem.The deformation is(described) for the elastic beam whose one end is simply supported and other is movable.Main results show that the problem has at least n positive solutions provided the "heights"are appropriate on some bounded sets(n is an arbitrary natural number).