东北师大学报(自然科学版)
東北師大學報(自然科學版)
동북사대학보(자연과학판)
JOURNAL OF NORTHEAST NORMAL UNIVERSITY(NATURAL SCIENCE EDITION)
2010年
1期
14-17
,共4页
奇异非线性三点边值问题%上下解%极大值原理%不动点定理
奇異非線性三點邊值問題%上下解%極大值原理%不動點定理
기이비선성삼점변치문제%상하해%겁대치원리%불동점정리
singular three-point boundary value problem%maximum principle%lower and upper solutions%fixed point%theorem
应用上下解方法和不动点定理,给出奇异二阶常微分方程三点边值问题｛x″(t)+(t,x(t))=0,t∈(0,1);x(0)=0,x(1)=kx(η)｝存在C[0,1]正解的充分条件.这里η∈(0,1)是一个常数,∈C((0,1)×[0,∞),[0,∞)).
應用上下解方法和不動點定理,給齣奇異二階常微分方程三點邊值問題｛x″(t)+(t,x(t))=0,t∈(0,1);x(0)=0,x(1)=kx(η)｝存在C[0,1]正解的充分條件.這裏η∈(0,1)是一箇常數,∈C((0,1)×[0,∞),[0,∞)).
응용상하해방법화불동점정리,급출기이이계상미분방정삼점변치문제｛x″(t)+(t,x(t))=0,t∈(0,1);x(0)=0,x(1)=kx(η)｝존재C[0,1]정해적충분조건.저리η∈(0,1)시일개상수,∈C((0,1)×[0,∞),[0,∞)).
By constructing lower and upper solutions and with the maximal
theorem,a sufficient condition for the existence of C［0,1］positive solutions is given to singular boundary value problems of a class of second order three-point sublinear differential equation ｛x″(t)+(t,x(t))=0,t∈(0,1);x(0)=0,x(1)=kx(η)｝. Where ∈(0,1)is a constant,∈C((0,1)×［0,∞),［0,∞)).
