一端简单支撑、另一端活动的非线性四阶边值问题的正解

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

摘要: 利用一个三阶两点边值问题的G reen函数和锥拉伸与锥压缩型的K rasnasel'sk ii不动点定理研究了一个非线性四阶边值问题正解存在性和多解性。描述了一端简单支撑,另一端活动的弹性梁的形变。结果表明:只要非线性项在某些有界集合上的“高度”是适当的,该问题至少有n个正解(n是一个任意的自然数)

Abstract: 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).