奇异三阶三点边值问题正解的存在性及多解性  

Existence and Multiplicity of Positive Solutions for SingularThird-Order Three-Point Boundary Value Problem

作　　者：武若飞 WU Ruofei(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）》2021年第4期816-820,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11671322).

摘　　要：用Krasnosel’skii不动点定理,给出奇异三阶三点边值问题u(t)+au′(t)=h(t)f(t,u(t)),t∈(0,π),u(0)=u′(η)=u″(π)=0,η∈[π/2,π),在权函数h(t)与非线性项f(t,u)均具有奇异性的情形下,其正解的存在性和多解性,其中a为正常数,η∈[π/2,π),h:(0,π)→[0,+∞)和f:(0,π)×(0,+∞)→(0,+∞)均为连续函数.By using the Krasnosel’skii fixed-point theorem,the author give the existence and multiplicity of positive solutions of a singular third-order three-point boundary value problem u(t)+au′(t)=h(t)f(t,u(t)),t∈(0,π),u(0)=u′(η)=u″(π)=0,η∈[π/2,π),in the case that both the weight function h(t)and the nonlinear term f(t,u)are singular,where a is positive constant,η∈[π/2,π),h:(0,π)→[0,+∞)and f:(0,π)×(0,∞)→[0,+∞)are continuous functions.

关 键 词：奇异性 正解 多解性 三阶三点边值问题 

分 类 号：O175.8[理学—数学]