大学数学
大學數學
대학수학
College Mathematics
2015年
5期
83-88
,共6页
四阶边值问题%闭凸锥%正解%凝聚映射%不动点指数
四階邊值問題%閉凸錐%正解%凝聚映射%不動點指數
사계변치문제%폐철추%정해%응취영사%불동점지수
fourth-order boundary value problem%closed convex cone%positive solution%condensing mapping%fixed point index
讨论了Banach空间E中的四阶边值问题 :u(4)(t) = f(t ,u(t)), 0 ≤ t ≤ 1 , u(0) = u(1) = u″(0) = u″(1) = θ正解的存在性 ,其中 f: 0 ,1 × P → P连续 ,P为E中的正元锥 .通过非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果 .
討論瞭Banach空間E中的四階邊值問題 :u(4)(t) = f(t ,u(t)), 0 ≤ t ≤ 1 , u(0) = u(1) = u″(0) = u″(1) = θ正解的存在性 ,其中 f: 0 ,1 × P → P連續 ,P為E中的正元錐 .通過非緊性測度的估計技巧與凝聚映射的不動點指數理論穫得瞭該問題正解的存在性結果 .
토론료Banach공간E중적사계변치문제 :u(4)(t) = f(t ,u(t)), 0 ≤ t ≤ 1 , u(0) = u(1) = u″(0) = u″(1) = θ정해적존재성 ,기중 f: 0 ,1 × P → P련속 ,P위E중적정원추 .통과비긴성측도적고계기교여응취영사적불동점지수이론획득료해문제정해적존재성결과 .
The existence of positive solutions for fourth-order boundary value problem u4 (t) = f (t ,u(t)), 0 ≤ t ≤ 1 , u(0) = u(1) = u″(0) = u″(1) = θ in Banach spaces E was discussed ,where f :0 ,1 × P→ Pis continuous ,and Pis the cone of positive elements in E .An existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping .
