左端刚性固定、右端简单支撑的奇异梁方程n个正解的存在性

摘要

利用锥上的Krasnosel'skii不动点定理,对于一个具有奇异非线性项的四阶两点边值问题建立了n个正解的存在性.在力学上该问题描述了左端刚性固定、右端简单支撑的弹性粱的挠曲.%By applying the Krasnosel'skii fixed point theorem on the cone,the existence of n positive solutions is established for a nonlinear fourth-order two-point boundary value problem with singular nonlinearity.In mechanics,the Droblem describes the deflection of an elastic beam rigidly fixed at left and simply supported at right.