西北师范大学学报(自然科学版)
西北師範大學學報(自然科學版)
서북사범대학학보(자연과학판)
JOURNAL OF NORTHWEST NORMAL UNIVERSITY(NATURAL SCIENCE)
2008年
4期
1-5
,共5页
广义Sturm-Liouville边界条件%Leray-Schauder延拓定理%多点边值问题
廣義Sturm-Liouville邊界條件%Leray-Schauder延拓定理%多點邊值問題
엄의Sturm-Liouville변계조건%Leray-Schauder연탁정리%다점변치문제
应用Leray-Schauder延拓定理,得到了二阶常微分方程多点边值问题x″(t)=f(t,x(t),x′(t))+e(t), t∈(0,1)αx(0)-βx′(0)=∑m-2i=1aix(ξi), γx(1)+δx′(1)=∑n-2j=1bjx(τj)解的存在性,其中f:[0,1]×R2R满足Caratheodory条件,e(·)∈L1(0,1),ai,bj∈R,ξi,τj∈(0,1),i=1,2,…,m-2,j=1,2,…,n-2,0<ξ1<ξ2<…<ξm-2<1,0<τ1<τ2<…<τn-2<1.
應用Leray-Schauder延拓定理,得到瞭二階常微分方程多點邊值問題x″(t)=f(t,x(t),x′(t))+e(t), t∈(0,1)αx(0)-βx′(0)=∑m-2i=1aix(ξi), γx(1)+δx′(1)=∑n-2j=1bjx(τj)解的存在性,其中f:[0,1]×R2R滿足Caratheodory條件,e(·)∈L1(0,1),ai,bj∈R,ξi,τj∈(0,1),i=1,2,…,m-2,j=1,2,…,n-2,0<ξ1<ξ2<…<ξm-2<1,0<τ1<τ2<…<τn-2<1.
응용Leray-Schauder연탁정리,득도료이계상미분방정다점변치문제x″(t)=f(t,x(t),x′(t))+e(t), t∈(0,1)αx(0)-βx′(0)=∑m-2i=1aix(ξi), γx(1)+δx′(1)=∑n-2j=1bjx(τj)해적존재성,기중f:[0,1]×R2R만족Caratheodory조건,e(·)∈L1(0,1),ai,bj∈R,ξi,τj∈(0,1),i=1,2,…,m-2,j=1,2,…,n-2,0<ξ1<ξ2<…<ξm-2<1,0<τ1<τ2<…<τn-2<1.