一类非线性二阶三点边值问题正解的存在性与多解性  

Existence and Multiplicity of Positive Solutions for a Class of Nonlinear Second-Order Three-Point Boundary Value Problems

作　　者：康聪聪 KANG Congcong(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1259-1265,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：用拓扑度理论和上下解方法考虑当非线性项f满足超线性增长条件时,非齐次二阶三点边值问题u″(t)+a(t)f(u(t))=0,t∈(0,1),u(0)=0,u(1)-αu(η)=b正解的存在性与多解性,结果表明,当参数b在不同取值范围内时,该问题至少存在两个正解、一个正解和无解.The author considered the existence and multiplicity of positive solutions of nonhomogeneous 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)=b by using topological degree theory and the method of upper and lower solutions when the nonlinear term f satisfied superlinear growth conditions.The results show that there are at least two positive solutions,one positive solution and no solution of the problem when the parameter b is in different value ranges.

关 键 词：三点边值问题 多解性 上下解 拓扑度理论 

分 类 号：O175.8[理学—数学]