数学的实践与认识
數學的實踐與認識
수학적실천여인식
MATHEMATICS IN PRACTICE AND THEORY
2011年
15期
212-221
,共10页
三点边值问题%正解%Leggett - williams不动点定理
三點邊值問題%正解%Leggett - williams不動點定理
삼점변치문제%정해%Leggett - williams불동점정리
研究一类半无穷区间上二阶微分方程三点边值问题(ρ(t)x'(t))' + f(t,x(t),x'(t)) =0 t∈ I =[0,+∞x(0) - βx' (0) =αx(ξ),x(+∞) =0其中ρ∈C[0,+∞)∩ C1(0,+∞),ρ(t)＞0,t∈I,(+∞∫) (1/p(t))dt＜∞,α≥0,β≥0,0＜ξ＜+∞ f:I×I×R→I.利用Leggett - williams不动点定理,我们获得了该边值问题至少存在三个正解的充分条件.
研究一類半無窮區間上二階微分方程三點邊值問題(ρ(t)x'(t))' + f(t,x(t),x'(t)) =0 t∈ I =[0,+∞x(0) - βx' (0) =αx(ξ),x(+∞) =0其中ρ∈C[0,+∞)∩ C1(0,+∞),ρ(t)＞0,t∈I,(+∞∫) (1/p(t))dt＜∞,α≥0,β≥0,0＜ξ＜+∞ f:I×I×R→I.利用Leggett - williams不動點定理,我們穫得瞭該邊值問題至少存在三箇正解的充分條件.
연구일류반무궁구간상이계미분방정삼점변치문제(ρ(t)x'(t))' + f(t,x(t),x'(t)) =0 t∈ I =[0,+∞x(0) - βx' (0) =αx(ξ),x(+∞) =0기중ρ∈C[0,+∞)∩ C1(0,+∞),ρ(t)＞0,t∈I,(+∞∫) (1/p(t))dt＜∞,α≥0,β≥0,0＜ξ＜+∞ f:I×I×R→I.이용Leggett - williams불동점정리,아문획득료해변치문제지소존재삼개정해적충분조건.
