东北师大学报(自然科学版)
東北師大學報(自然科學版)
동북사대학보(자연과학판)
JOURNAL OF NORTHEAST NORMAL UNIVERSITY(NATURAL SCIENCE EDITION)
2010年
1期
5-9
,共5页
奇异混合单调算子%不动点定理%边值问题%p-Laplacian算子
奇異混閤單調算子%不動點定理%邊值問題%p-Laplacian算子
기이혼합단조산자%불동점정리%변치문제%p-Laplacian산자
singular mixed monotone operator%fixed point theorem%boundary value problems%p-Lapacian operator
利用混合单调算子,给出了奇异四阶差分方程边值问题｛Δ~2[φ_p(Δ~2y(i-1))]+λF(i,y(i))=0, i∈[1,T+3],λ＞0;y(0)=y(T+4)=0;Δ~2y(0)=Δ~2y(T+2)=0｝正解的存在唯一性,其中φ_p(s)=|s|~( p-2) s,p＞1,F∈C((0,T+4)×(0,+∞),(0,+∞)),[1,T+3]=1,2,…,T+3,[0,T+4]=0,1,2,…,T+4,并且非线性项F在y=0可能是奇异的.
利用混閤單調算子,給齣瞭奇異四階差分方程邊值問題｛Δ~2[φ_p(Δ~2y(i-1))]+λF(i,y(i))=0, i∈[1,T+3],λ＞0;y(0)=y(T+4)=0;Δ~2y(0)=Δ~2y(T+2)=0｝正解的存在唯一性,其中φ_p(s)=|s|~( p-2) s,p＞1,F∈C((0,T+4)×(0,+∞),(0,+∞)),[1,T+3]=1,2,…,T+3,[0,T+4]=0,1,2,…,T+4,併且非線性項F在y=0可能是奇異的.
이용혼합단조산자,급출료기이사계차분방정변치문제｛Δ~2[φ_p(Δ~2y(i-1))]+λF(i,y(i))=0, i∈[1,T+3],λ＞0;y(0)=y(T+4)=0;Δ~2y(0)=Δ~2y(T+2)=0｝정해적존재유일성,기중φ_p(s)=|s|~( p-2) s,p＞1,F∈C((0,T+4)×(0,+∞),(0,+∞)),[1,T+3]=1,2,…,T+3,[0,T+4]=0,1,2,…,T+4,병차비선성항F재y=0가능시기이적.
By means of a fixed point theorem,existence and uniqueness of positive solutions for four-order four-point nonlinear singular discrete boundary value problems with p-Lapacian operator.The theorems obtained are very general and complement previous known results.
