吉林大学学报（理学版）2025，Vol.63Issue(6)：1565-1571,7.DOI:10.13413/j.cnki.jdxblxb.2025010
不定半正Sturm-Liouville边值问题正解的存在性
Existence of Positive Solutions for Uncertain Semipositive Sturm-Liouville Boundary Value Problems
摘要
Abstract
The author considers the existence of positive solutions for the boundary value problems of a class of singular second-order ordinary differential equations{-u"=λh(t)f(u),t∈(0,1)αu(0)-βu′(0)=0,γu(1)+δu′(1)=0,where α,β,γ,δ≥0 are constants,λ＞0 is a parameter,h∈L1((0,1),[0,+∞)),f∈C((0,+∞),R)and singular at zero,satisfying the condition of superlinear growth at infinity.Based on the Krasnoselskii fixed point theorem,the author proves that there exists a constant λ0＞0,such that the problem has at least one positive solution when λ∈(0,λ0).关键词
正解/半正问题/奇异边值问题/锥Key words
positive solution/semipositive problem/singular boundary value problem/cone分类
数理科学引用本文复制引用
卢睿..不定半正Sturm-Liouville边值问题正解的存在性[J].吉林大学学报（理学版）,2025,63(6):1565-1571,7.基金项目
国家自然科学基金(批准号:12061064). （批准号:12061064）
