一类格林函数变号的二阶Neuman问题正解的存在性  

Existence of Positive Solutions for a Class of Second Order Neumann Problem with Sign-Changing Green′s Function

作　　者：李朝倩 LI Zhao-qian(School 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：《西南师范大学学报（自然科学版）》2020年第12期43-47,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671322).

摘　　要：运用Schauder不动点定理研究了一类格林函数变号的非线性二阶Neumann问题u″+m^2u=λg(t)f(u)t∈[0,1]u′(0)=u′(1)=0正解的存在性,其中λ是一个正参数,m∈π/2,π/2+ε,ε>0充分小,g:[0,1]R+为连续函数,f:[0,∞)R为连续函数且f(0)>0.In this paper,a class of second-order nonlinear Neumann problems has been studied with sign-changing Green′s function u″+m^2u=λg(t)f(u)t∈[0,1]u′(0)=u′(1)=0 Whereλis a positive parameter,m∈π/2,π/2+εwithε>0 small,g:[0,1]R+is a continuous function,f:[0,∞]R is a continuous function and f(0)>0.by means of the Schauder fixed point theorem,We obtain the existence of positive solutions.

关 键 词：NEUMANN问题 格林函数 正解 存在性 

分 类 号：O177.92[理学—数学]