摘要
本文的主要结果为：若f(t,u):(0,1)×(0,+∞→[0，+∞）连续，关于u单调减少，存在实数b＞0使对任意0＜r＜1有（0，1）×（0，∞），则奇异二阶边值问题有正解的充要条件为，有C1[0，1]正解的充分必要条件为其中α，β，σ，γ是非负实效，且为所述边值问题的Green函数．
Main results of this paper as follows: Suppose f(t,u): (O, 1) x (0, +∞) →[0,+∞) is continuous, is dereasing on u; there erists real number b > 0 such thatf(t, ru) ≤ r-b f(t,u) for any 0 < r < 1 and (t, u) ∈ (0, 1) x (0, ∞). Then, a necessaryand sufficient conditinn for the Singular second order boundary problemto have positive solutions is 0 < ∫01 G(s,s)f(s, 1)ds < ∞, a necessary and sufficientcondition for that to have C1[0, 1] positive solution is 0 <∫01 f(s,G(s, s))ds < ∞.Where α, β, δ, γ are nonnegative real numbers and αγ +αδ+ βγ > 0, G(t, s) is Green'sfunction of the corresponding boundary value problem.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2000年第1期179-188,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金!19871047
山东省自然科学基金!Y97A12017
关键词
奇异边值问题
正解
奇异微分方程
非线性
Singular boundary value problem
Positive solution
Necessary and sufficient condition
