四阶两点非齐次边值问题正解的唯一性及对参数依赖性  

Uniqueness and parameter dependence of positive solutions of fourth-order second-point nonhomogeneous BVPs

作　　者：沈文国 孙建仁 包理群 SHEN Wenguo;SUN Jianren;BAO Liqun(Department of Basic Courses, Lanzhou Institute of Technology, Lanzhou 730050, China;College of Mechano-Electronic Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China;College of Electronic and Information Engineering, Lanzhou Institute of Technology, Lanzhou 730050, China)

机构地区：[1]兰州工业学院基础学科部,兰州730050 [2]兰州工业学院机电工程学院,兰州730050 [3]兰州工业学院电子信息工程学院,兰州730050

出　　处：《华中师范大学学报（自然科学版）》2021年第3期343-346,364,共5页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11561038);甘肃省自然科学基金项目(20JR5RA377);兰州工业学院‘开物’科研创新团队支持计划项目(2018KW-03).

摘　　要：利用单调混合算子理论,研究了四阶两点非齐次边值问题:x′′′′t+f(t,x)=0,t∈0,1,x0=α,x′0=β,x1=λ,x′1=-μ正解的存在性与唯一性问题,其中,α>0,β>0,λ>0,μ>0,f(t,x)∈C([0,1]×[0,∞),[0,∞)),f(t,x)对于x单调递增,并且存在0≤θ<1使得f(t,kx)≥kθf(t,x),t∈[0,1],k∈[0,1],x∈[0,∞)成立.给参数α,β,λ,μ赋予一定的条件,证明了上述问题存在唯一正解,并且研究了解对参数的依赖性.In this paper,by using the mixed monotone operator theory in cones,the fourth-order second-point nonhomogeneous boundary-value problem is investigated:x′′′′t+f(t,x)=0,t∈0,1,x0=α,x′0=β,x1=λ,x′1=-μ,whereα>0,β>0,λ>0,μ>0,f(t,x)∈C([0,1]×[0,∞),[0,∞))is continuous and monotonically increasing for x.There exists 0≤θ<1 such that f(t,kx)≥kθf(t,x),t∈[0,1],k∈[0,1],x∈[0,∞).The existence and uniqueness of a positive solution and for the above problem is proved and the dependence of this solution on the parametersα,β,λandμis studied.

关 键 词：四阶两点非齐次边值问题 正解 唯一性 解对参数的依赖性 单调混合算子理论 

分 类 号：O175.8[理学—数学]