分数阶混合差分方程边值问题解的存在性(英文)

The existence of solutions for the boundary value problem of fractional hybrid difference equation

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.

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 .