一类非线性三阶三点边值问题正解的全局结构  

Global Structure of Positive Solutions for a Class of Nonlinear Third-Order Three-Point Boundary Value Problems

作　　者：张瑞燕 ZHANG Ruiyan(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：《吉林大学学报（理学版）》2022年第6期1273-1279,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12061064)。

摘　　要：用Krein-Rutman定理和Dancer全局分歧理论研究非线性三阶三点边值问题u(t)+rf(t,u(t))=0,t∈(0,1),u(0)=αu′(0),u(1)=βu(η),u′(1)=0正解的全局结构,其中r>0是一个参数,0<η<1,α,β>0,且非线性项f∈C([0,1]×[0,∞),[0,∞))在0处和∞处均满足渐近线性增长条件.By using the Krein-Rutman theorem and Dancer global bifurcation theory,the author studies the global structure of positive solutions for nonlinear third-order three-point boundary value problem u(t)+rf(t,u(t))=0,t∈(0,1),u(0)=αu′(0),u(1)=βu(η),u′(1)=0,where r>0 is a parameter,0<η<1,α,β>0,and the nonlinear term f∈C([0,1]×[0,∞),[0,∞))satisfies asymptotic linear growth condition at 0 and∞.

关 键 词：多点边值问题 正解 全局结构 分歧定理 

分 类 号：O175.8[理学—数学]