一类二阶奇异微分方程边值问题正解的存在性  

Existence of Positive Solutions for a Class of Second-Order Singular Differential Equation Boundary Value Problems

作　　者：蒋玲芳[1] 何志乾[2] 苗亮英[3] JIANG Ling-fang;HE Zhi-qian;MIAO Liang-ying(Department of Mathematics,Leshan Vacationnal and Technical College,Leshan 614000,China;Department of Mathematics,Qinghai University,Xining 810016,China;School of Mathematics and Statistics,Qinghai Minzu University,Xining 810007,China)

机构地区：[1]乐山职业技术学院数学教研室,四川乐山614000 [2]青海大学数理学院,青海西宁810016 [3]青海民族大学数学与统计学院,青海西宁810007

出　　处：《数学的实践与认识》2023年第7期206-211,共6页Mathematics in Practice and Theory

基　　金：青海省自然科学基金项目(2021-ZJ-957Q);青海大学校级教育教学项目(JY202138)。

摘　　要：研究一类二阶奇异微分方程边值问题{-u''=h(t)f(u),u(0)=0,u'(1)+c(u(1)u(1)=0正解的存在性,其中f∈C([0,∞),[0,∞)),c∈C([0,∞),[0,∞)),且h∈C((0,1],[0,∞))在t=0处允许有奇性.运用锥拉伸与压缩不动点定理,证明了当非线性项f在原点和无穷远处分别满足超线性和次线性增长条件时,上述问题至少存在一个正解.所得结果不仅可推广已有工作的相关结果,也为更好地研究这类问题的定性性质提供了理论依据.In this paper,we are considered with the existence of positive solutions for a class of second-order singular boundary value problem{-u''=h(t)f(u),u(0)=0,u'(1)+c(u(1)u(1)=0where f∈C([0,∞),[0,∞)),c∈C([0,∞),[0,∞)),and h∈C((0,1],[0,∞)),and h is allowed to be singular at t=O.By using the fixed-point theorem of cone expansion-compression,we prove that there is at least one positive solution to this problem when the nonlinear term f satisfies superlinear and sublinear growth conditions at the origin and at infinity,respectively.The results obtained in this paper can not only extend the related results of previous work,but also provide a theoretical basis for better research on the qualitative nature of this kind of problems.

关 键 词：非线性边界条件 正解 存在性 锥 

分 类 号：O175.8[理学—数学]