带变系数的四阶微分方程正解的存在性  

Existence of Positive Solutions to Fourth-order Differential Equations with Variable Coefficients

作　　者：康宏亮 KANG Hong-liang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《兰州文理学院学报（自然科学版）》2018年第4期27-31,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金(71261023)

摘　　要：考虑了如下带变系数的四阶微分方程{u^(4)-m^4 u=λa(x)f(u),x∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0正解的存在性.其中m为常数,a∶[0,1]→R,f∶R^+→R连续,f(0)>0,λ>0为参数.主要结果的证明基于Leary-Schauder不动点理论.In this paper,the existence of positive solutions to fourth-order differential equations with variable coefficients is considered as follows：{u^（4）-m^4u=λa（x）f（u）,x ∈（0,1）,u（0）=u（1）=u″（0）=u″（1）=0 Wheremis a constant,a∶[0,1]→R,f∶R→R is continuous,f（0）0 andλ0 are parameters.The proof of the main results is based on the Leray-Schauder fixed point theory.

关 键 词：GREEN函数 Leray-Schauder不动点理论 存在性 

分 类 号：O175.8[理学—数学]