一类二阶奇异微分方程正解的存在唯一性  

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR A CLASS OF SECOND ORDER SINGULAR DIFFERENTIAL EQUATIONS

作　　者：赵增勤[1] 

机构地区：[1]曲阜师范大学数学科学学院,曲阜273165

出　　处：《系统科学与数学》2008年第3期325-333,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10471075);山东省自然科学基金(Y2006A04);高教博士点专项科研基金(20050446001)资助课题.

摘　　要：利用上下解方法、不动点理论研究奇异微分方程u″+f(t,u)=0,t∈(0,1)在边界条件αu(0)-βu′(0)=0,γu(1)+δu′(1)=0下C[0,1]正解和C^1[0,1]正解的存在性与唯一性.其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.The existence of positive solutions for a class of singular boundary value problems is investigated. Furthermore, the sufficient condition for the existence and uniqueness of positive solution of the system in C[0, 1] and C1 [0, 1] is given respectively, by means of the method of lower and upper solution, and the fixed point theorem.

关 键 词：奇异边值问题 正解 上下解 不动点定理. 

分 类 号：O175.2[理学—数学] O175.8[理学—基础数学]