系统科学与数学
繫統科學與數學
계통과학여수학
JOURNAL OF SYSTEMS SCIENCE AND MATHEMATICAL SCIENCES
2010年
1期
118-128
,共11页
正解%n-阶m-点奇异边值问题%不动点定理.
正解%n-階m-點奇異邊值問題%不動點定理.
정해%n-계m-점기이변치문제%불동점정리.
Positive solution%nth-order m-point singular boundary value problem%fixed point theorem.
研究n-阶m-点奇异边值问题{u~((n))(t)+h(t)f(t,t(t),u1(t),…,u~((n-2))(t))=0,0＜t＜1,u(0)=u'(0)=…=u~((n-2))(0)=0,u~((n-2))(1)=∑_(i=1)~(m-2) kiu~((n-2))(ξ_i),其中h(t)允许在t=0,t=1处奇异,f(t,v_o,v_1,…,v_(n-2))允许在vi=0(i=0,1,…,n-2)处奇异.利用锥拉伸与压缩不动点定理得到了上述奇异边值问题正解的存在性.
研究n-階m-點奇異邊值問題{u~((n))(t)+h(t)f(t,t(t),u1(t),…,u~((n-2))(t))=0,0＜t＜1,u(0)=u'(0)=…=u~((n-2))(0)=0,u~((n-2))(1)=∑_(i=1)~(m-2) kiu~((n-2))(ξ_i),其中h(t)允許在t=0,t=1處奇異,f(t,v_o,v_1,…,v_(n-2))允許在vi=0(i=0,1,…,n-2)處奇異.利用錐拉伸與壓縮不動點定理得到瞭上述奇異邊值問題正解的存在性.
연구n-계m-점기이변치문제{u~((n))(t)+h(t)f(t,t(t),u1(t),…,u~((n-2))(t))=0,0＜t＜1,u(0)=u'(0)=…=u~((n-2))(0)=0,u~((n-2))(1)=∑_(i=1)~(m-2) kiu~((n-2))(ξ_i),기중h(t)윤허재t=0,t=1처기이,f(t,v_o,v_1,…,v_(n-2))윤허재vi=0(i=0,1,…,n-2)처기이.이용추랍신여압축불동점정리득도료상술기이변치문제정해적존재성.
In this paper,by using Krasnosel'skill fixed point theorem,the existence result of positive solutions is established for the following nth-order m-point singular boundary value problem:{u~((n))(t)+h(t)f(t,t(t),u1(t),…,u~((n-2))(t))=0,0＜t＜1,u(0)=u'(0)=…=u~((n-2))(0)=0,u~((n-2))(1)=∑_(i=1)~(m-2) kiu~((n-2))(ξ_i),where h(t) can be singular at t=0,t=1,f(t,v_0,v_1,…,v_(n-2))may also be singular at v_i=0(i=0,1…,n-2).
