摘要
设p(t) ,q(t)∈C((0 ,1) ,(0 ,+∞ ) ) ,f(x) ,g(y)∈ ((0 ,+∞ ) ,(0 ,+∞ ) ) ,并且满足下列条件 :(1) f(x)是x的减函数 ,存在正数b >0 ,使得 f(rx)≤r-bf(x) ,对任意 (r ,x)∈ (0 ,1)× (0 ,+∞ ) ,limx→ 0 +xbf(x) >0 ;(2 ) g(y)是y的减函数 ,limy→ 0 +g(y) =+∞ .则下列奇异边值问题x″ +p(t) f(x) +q(t) g(x′) =0 ,0 <t<1,x(0 ) =x′(1) =0 .有唯一C1[0 ,1]正解的充分必要条件是 :t-bp(t)∈L1[0 ,1],q(t)∈L1[0 ,1].
Let p(t),q(t)∈C((0,1),(0,+∞)),f(x),g(y)∈C((0,+∞),(0,+∞)) and the following conditions are satisfied: (1)f(x) is decreasing in x ,there exists a constant number b>0 such that f(rx)≤r -b f(x) ,for any (r,x)∈(0,1)×(0,+∞) and lim x→0 +x bf(x)>0;(2)g(y) is decreasing in y and lim y→0 +g(y)=+∞ .Then a necessary and sufficient condition to have unique positive C 1 solution for the singular boundary value problem x″+p(t)f(x)+q(t)g(x′)=0,0<t<1, x(0)=x′(1)=0, is t -b p(t)∈L 1 and q(t)∈L 1.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2001年第5期630-634,共5页
Journal of Sichuan University(Natural Science Edition)
