一类半正二阶Neumann边值问题正解的存在性  

Existence of positive solutions for a class of semipositone second order Neumann boundary value problems

作　　者：雷想兵 LEI Xiang-bing(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,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：《山东大学学报（理学版）》2023年第4期82-88,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12061064)。

摘　　要：考察一类半正二阶Neumann边值问题{u"(t)+a(t)u(t)=λf(t,u(t)),0<t<l,u'(0)=u(1)=0正解的存在性,其中λ是正参数,a∈C[0,1]且0<a(t)<π^(2)/4,f∈C([0,1]×R^(+),R)且f(t,0)<0。证得存在一个正数λ_(0),使得当0<λ<λ_(0)时,该问题存在一个正解。主要结果的证明基于拓扑度理论。This paper considers the existence of positive solutions of second order Neumann boundary value problems{u"(t)+a(t)u(t)=λf(t,u(t)),0<t<l,u'(0)=u(1)=0,where λ is a positive parameter,a∈C[0,1]and 0<a(t)<π^(2)/4,f∈C([0,1]×R^(+),R)and f(t,0)<0.The proof of that there exists a positive constant Ao such that the problem has one positive solution for 0<λ<λ_(0).The proof of the main results is based on topological degree theory.

关 键 词：NEUMANN边值问题 正解 半正 拓扑度 

分 类 号：O175.8[理学—数学]