四阶两点边值问题3个对称正解的存在性  

The Existence of Three Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem

作　　者：达举霞 DA Juxia(Changqing College of Lanzhou University of Finance and Economics,Lanzhou 730070,China)

机构地区：[1]兰州财经大学长青学院,兰州730070

出　　处：《华南师范大学学报（自然科学版）》2021年第1期90-93,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11561063)。

摘　　要：应用广义的Leggett-Williams不动点定理,研究了四阶两点边值问题u(4)(t)=f(u(t))(t∈[0,1]),u(0)=u(1)=0,u″(0)=u″(1)=0正解的存在性,其中f:R→[0,+∞)连续.在f满足适当的增长条件下,得到该问题至少存在3个对称正解.Applying the generalized Leggett-Williams fixed-point theorem,the existence of positive solutions to the fourth-order boundary value problem is studied:u(4)(t)=f(u(t)),t∈[0,1],u(0)=u(1)=0,u″(0)=u″(1)=0,where f:R→[0,+∞) is continuous.Under some conditions on f,there exist at least three symmetric positive solutions.

关 键 词：四阶边值问题 格林函数 对称正解 锥 

分 类 号：O175.8[理学—数学]