不可分离变量奇异非线性Sturm-Liouville问题的正解  

Positive Solutions of Singular NonlinearSturmLiouville Problems

作　　者：刘汝臣[1] 

机构地区：[1]辽宁省交通高等专科学校基础部,辽宁沈阳110122

出　　处：《沈阳理工大学学报》2006年第2期80-83,共4页Journal of Shenyang Ligong University

摘　　要：本文研究了如下情形Sturm-Liouville问题-(Lφ)(x)=f(x,φ(x)),0<x<1R1(φ)=α1φ(0)+1βφ′(0)=0R2(φ)=α2φ(1)+2βφ′(1)=0的正解情况,并给出了相应的例子.其中,(Lφ)(x)=(p(x)φ(′x))′+q(x)φ(x),p(x)∈C1[0,1],p(x)>0,q(x)∈C[0,1],q(x)≤0;α1,α2,β2≥0,1β≤0.不仅允许h(x)在x=0,x=1处奇异,而且f(t,u)≤h(t)m(u),h:(0,1)→[0,+∞)连续,m:[0,+∞)→[0,+∞)连续.推广了文献[1]的结果.The positive solutions of the singular nonlinear Sturm-Liouville problems-(Lφ)(x)=f(x,φ(x)),0<x<1R_1(φ)=α_1φ(0)+β_1φ′(0)=0R_2(φ)=α_2φ(1)+β_2φ′(1)=0are studied,and the corresponding examples are given,where(Lφ)(x)=(p(x)φ′(x))′+q(x)φ(x),p(x)∈C^1,p(x)>0,q(x)∈C,q(x)≤0;α_1,α_2,β_2≥0,β_1≤0.Not only h(x)is allowed to be singular at x=0 and x=1,but also f(t,u)≤h(t)m(u),h:(0,1)→[0,+∞) is continuous and m:[0,+∞)→[0,+∞) is continuous.The conclusions is to extend and improve the main results of literature[1].

关 键 词：奇异非线性Sturm-Liouville问题 全连续 正解 锥 不动点指数 

分 类 号：O175.1[理学—数学]