非线性项带导数的三点边值问题正解的存在性与多解性  

Existence and Multiplicity of Positive Solutions for Three-point Boundary Value Problems with Derivatives of Nonlinear Terms

作　　者：康宏亮 肖鸿民 KANG Hongliang;XIAO Hongmin(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu)

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：《四川师范大学学报（自然科学版）》2019年第2期194-198,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(71261023)

摘　　要：基于锥上的不动点理论,考虑非线性项带导数的二阶三点边值问题■,正解的存在性及多解性,其中f:[0,∞)→[0,∞)为连续函数,0<α<1,0<η<1,0<αη<1.In this paper,we study the existence and multiplicity of positive solutions for secondorder threepoint boundary value problems{u″(t)+a(t)f(u′(t))=0,t∈[0,1],u′(0)=0,u(1)=αu(η)with derivatives of nonlinear terms,where f:[0,∞)→[0,∞)is continuous,0<α<1,0<η<1,0<αη<1.The proof of the main results is based on the fixed point index theory.

关 键 词：三点边值问题 正解 多解性 不动点指数 存在性 

分 类 号：O175.8[理学—数学]