一类四阶非线性微分方程两点边值问题的正解  

Positive Solutions of Two-point Boundary value Problems for Fourth-order Nonlinear Differential Equation

作　　者：陆海霞[1] 孙经先[2] 

机构地区：[1]宿迁学院教师教育系,江苏宿迁223800 [2]江苏师范大学数学科学学院,江苏徐州221116

出　　处：《数学的实践与认识》2014年第8期229-235,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10971179);宿迁学院科研基金(2011KY10)

摘　　要：应用锥理论和不动点指数方法,在与相应的线性算子第一特征值有关的条件下,获得了一类四阶非线性常微分方程两点边值问题{-u(4)(t)t=f(t,u(t)),≤t≤1,u(0)=u′(0)=u′(1)=u′″(1)=0正解的存在性.By applying the theory of fixed point index and the cone theory, the existence of positive solutions of two-point boundary value problems for the fourth-order nonlinear differential equation {-u（4）（t）=f（t,u（t））,0〈t〈1,u（0）=u＇（0）=u＇（1）=u＇＇＇（1）=0 is considered under some conditions concerning the first eigenvalue corresponding to the rele- vant linear operator.

关 键 词：非线性边值问题 正解 不动点指数 锥 

分 类 号：O175.8[理学—数学]