二阶三点边值问题对称正解的存在性及多解性  

Existence and multiplicity of symmetric positive solutions for second-order three-point boundary value problem

作　　者：张静 韩晓玲 ZHANG Jing;HAN Xiao-Ling(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,兰州730070

出　　处：《四川大学学报（自然科学版）》2018年第5期935-940,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11561063)

摘　　要：本文运用Krasnosel'skii不动点定理方法研究了三点边值问题{u″(t)+a(t)f(t,u,u′)=0,t∈[0,1],u(0)=u(1)=αu(η)对称正解的存在性和多解性,这里α∈(0,1),η∈(0,1),f:[0,1]×[0,∞)×(-∞,∞)→[0,∞)连续,且对任意(u,v)∈[0,∞)×(-∞,∞),f(·,u,v)在[0,1]上对称.By using the fixed point theorem of Krasnosel'skii,we study the existence and multiplicity of symmetric positive solutions for the following second-order three-point boundary value problem u″(t)+a(t)f(t,u,u′)=0,t∈[0,1],u(0)=u(1)=αu(η),whereα∈(0,1),η∈(0,1),f:[0,1]×[0,∞)×(-∞,∞)→[0,∞)is continuous,f(·,u,v)is symmetric on[0,1]for all(u,v)∈[0,∞)×(-∞,∞).

关 键 词：三点边值问题 对称正解 不动点定理 

分 类 号：O175.8[理学—数学]