一类四阶边值问题的n个正解的存在性

把锥压缩与锥拉伸型的Krasnosel'skii不动点定理用于一类含有二阶导数的非线性四阶两点边值问题并且获得了n个正解的存在性，其中，n是一个任意的自然数，这是首次考察它的任意n个解的存在性．此类四阶边值问题通常描述两端简单支撑的弹性梁的平衡状态．将处理二阶方程的局部化方法使用于这一类问题取得了成功．这里所说的局部化方法是指通过考察非线性项在有界集上的性质决定解的存在性的方法．在具体的操作上，使用了方程组技巧，即把四阶方程转化为一个积分方程组．最大优点是实现了判断条件的数值化，从而使用起来比较方便．

Exisence of n Positive Solutions for a Class of Fourth-order Boundary Value Problems

We apply Krasnosel'skii fixed point theorem of cone expansion compression type to a class of nonlinear fourth order two point boundary value problems with second derivative, and obtain existence of n positive solutions, where n is an arbitrary natural number. This class of problems usually describes the equilibrium state of elastic beam whose both ends are simply supported.