含有2个参数的非线性四阶边值问题解的一个存在定理
An existence theorem of solution to nonlinear fourth-order boundary value problems with two parameters
-
摘要: 通过选择适当的Banach空间并且利用Leray-Schauder非线性抉择,对含有2个参数及各阶导数一类非线性四阶两点边值问题建立了一个存在定理.在此项工作中,非线性项满足某种函数型线性增长条件.在材料力学上,这类问题描述了2个端点被简单支撑的弹性梁的形变.Abstract: By choosing suitable Banach space and using Leray-Schauder nonlinear alternate,an existence theorem is established for a class of nonlinear fourth-order boundary value problems with two parameters and all order derivatives.In this work,the nonlinear term satisfies a linear growth condition of function type.In material mechanics,the class of problems describes the deformations of an elastic beam simply supported at both ends.