非线性项含有变号一阶导数的四阶边值问题

A Fourth-Order Boundary Value Problem whose Nonlinearity Contains Changing-Sign First Derivative

考察了一个四阶两点边值问题的正解,它的非线性项含有变号的一阶导数.通过利用锥压缩与锥拉伸型的Krasnosel′skii不动点定理证明了几个存在性与多解性定理.特别地,只要非线性项的主要部分在某些有界集合上的高度适当,这个问题能够具有n个正解,其中n是一个任意的自然数.

The positive solutions are considered for a fourth-order two-point boundary value problem whose nonlinearity contains changing-sign first derivative. By applying the Krasnosellskii fixed point theorem of cone expansion-compression type,several existence and multiplicity theorems are proved. Particularly,the problem can have n positive solutions if the heights of principle part of nonlinearity are appropriate on some bounded sets. Here n is an arbitrary natural number.