四川大学学报(自然科学版)
四川大學學報(自然科學版)
사천대학학보(자연과학판)
JOURNAL OF SICHUAN UNIVERSITY(NATURAL SCIENCE EDITION)
2013年
6期
1199-1204
,共6页
分数阶差分方程%边值问题%解的存在性
分數階差分方程%邊值問題%解的存在性
분수계차분방정%변치문제%해적존재성
fractional difference equation%boundary value problem%existence of solution
本文研究分数阶混合差分方程边值问题Δν x(t)f (t ,x(t))= g(t+ν-1,x(t+ν-1)), x(ν-2)= x(ν+ b)=0解的存在性,其中 g ∈ C([ν-1,ν+ b -1]Nν-1× R ,R),f ∈C([ν-2,ν+ b]Nν-2× R ,R\{0})且1<ν≤2.我们给出该问题解的表达式,并运用布劳威尔不动点定理和上下解方法得到了解的两个存在性定理.
本文研究分數階混閤差分方程邊值問題Δν x(t)f (t ,x(t))= g(t+ν-1,x(t+ν-1)), x(ν-2)= x(ν+ b)=0解的存在性,其中 g ∈ C([ν-1,ν+ b -1]Nν-1× R ,R),f ∈C([ν-2,ν+ b]Nν-2× R ,R\{0})且1<ν≤2.我們給齣該問題解的錶達式,併運用佈勞威爾不動點定理和上下解方法得到瞭解的兩箇存在性定理.
본문연구분수계혼합차분방정변치문제Δν x(t)f (t ,x(t))= g(t+ν-1,x(t+ν-1)), x(ν-2)= x(ν+ b)=0해적존재성,기중 g ∈ C([ν-1,ν+ b -1]Nν-1× R ,R),f ∈C([ν-2,ν+ b]Nν-2× R ,R\{0})차1<ν≤2.아문급출해문제해적표체식,병운용포로위이불동점정리화상하해방법득도료해적량개존재성정리.
We study the existence of solutions for the boundary value problem of fractional hybrid differ-ence equation Δν x(t)f (t ,x(t)) = g(t + ν- 1 ,x(t + ν- 1)) ,x(ν- 2) = x(ν+ b) = 0 ,w here g ∈C([ν-1 ,ν+ b -1]Nν-1 × R ,R) ,f ∈ C([ν-2 ,ν+ b]Nν-2 × R ,R\{0}) and 1 < ν≤ 2 .We give a represen-tation for the solution to this problem .By using the Brouwer theorem and the upper and lower solutions method ,two existence theorems to this problem are proved .