一类二阶非齐次边值问题正解的存在性与多解性  

Existence and multiplicity of positive solutions for a class of second-order nonhomogeneous boundary value problems

作　　者：石轩荣 SHI Xuanrong(College 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,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2023年第1期38-42,共5页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12061064)。

摘　　要：研究了二阶非齐次边值问题{-u″(t)+k^(2)u(t)=f(u(t)),t∈[0,],正解的存在性与多解性,其中k,b>0为常数,f∈C([0,∞),[0,∞)),f_(0):=lim_(u→0^(+))f(u)/u=0,f_(∞):=lim_(u→∞)f(u)/u=∞.运用上下解方法和拓扑度理论,证明了存在常数b^(*)>0,使得当0<b<b^(*)时,该问题不存在2个正解;当b=b^(*)时,该问题存在1个正解。We are concerned with existence and multiplicity of positive solutions for the second-order nonhomogeneous boundary value problem{-u″(t)+k^(2)u(t)=f(u(t)),t∈[0,1],where k,b>0 are constants,f∈C([0,∞),[0,∞)),andf_(0):=lim_(u→0^(+))f(u)/u=0,f_(∞):=lim_(u→∞)f(u)/u=∞.We adopt the method of upper and lower solutions and the topological degree theory to prove that there exists b^(*)>0,such that the problem above has zero,one and two positive solutions corresponding respectively to b>b^(*),b=b^(*)and 0^(*).

关 键 词：正解 多解性 上下解方法 拓扑度理论 

分 类 号：O175.8[理学—数学]