一类弹性梁方程的正解存在性与多解性

Existence and multiplicity of positive solutions to a class of elastic beam equations

通过选择合适的锥并利用锥拉伸与锥压缩型的Krasnosel’sii不动点定理考察了一类一端简单支撑 ,另一端被滑动夹子夹住的四阶弹性梁方程的n个正解的存在性 .这里n是一个任意的自然数 .结论的主要条件是局部的 .换言之 ,如果非线性项在某些有界集上的“高度”是适当的 。

By choosing suitable cone and using the Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of n positive solutions was considered for a class of elastic beam equations where one end is simply supported and other is clamped by sliding clamps. Here,n is an arbitrary natural number. The main conditions of the results are local. In another word, the equation may have n positive solutions provided the “heights” of nonlinear term are appropriate on some bounded sets.