一类两点边值问题的正解个数  

EXACT NUMBER OF POSITIVE SOLUTIONS FOR A CLASS OF TWO-POINT BOUNDARY VALUE PROBLEMS

作　　者：程建纲[1] 

机构地区：[1]烟台大学数学系,山东烟台264005

出　　处：《数学年刊（A辑）》2004年第3期279-284,共6页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10071066;N0.10251002);山东省自然科学基金(No.Y2002A10)资助的项目

摘　　要：本文讨论边值问题y''+λ(yp+μp+yp)=0,y(-1)=y(1)=0,其中λ>0是正参数,μ≥0.对(1-p)(1-q)>0的情形得出了正解的存在唯一性.对(1-p)(1-q)<0的情形,其主要结论是:若p>1>q>-(25+23p)/(23+25p),μ≥0,则存在λ*>0,使得当0<λ<λ*时,此边值问题恰好存在两个正解,当λ=λ*时,存在唯一正解,当λ>λ*时,不存在正解.This paper considers the boundary value problem y' + λ(yp + nμ + yq) = 0 and y(-1) = y(1) = 0, where A > 0 is a positive parameter and μ≥ 0. The uniqueness of positive solutions is obtained for the case of (1 - p)(1 - q) > 0. For the case of (1 - p)(1 - q) < 0, the main result as follows: if μ ≥ 0 and p> >>(25 + 23p)/(23 + 25p), then there exists λ > 0 such that this problem has exactly two positive solutions for 0 < λ < λ*, exactly one for λ = λ* and none for λ >?.

关 键 词：边值问题 正解 存在性 

分 类 号：O175.8[理学—数学]