具有p-Laplacian算子的delta-nabla分数阶差分边值问题正解的存在性

Existence of positive solutions for p-Laplacian fractional difference involving the discrete delta-nabla fractional boundary value problem

考虑具有p-Laplacian算子的delta-nabla分数阶差分方程边值问题:■其中b∈Z+,T=[α-β-1,b+α-β-1]Να-β-1, 1≤α,β≤2, 3<α+β≤4, 0<ω<1,λ∈(0,+∞),Δ■和b?α分别是左右分数阶差分算子,并且■.利用上下解方法和Schauder不动点定理,得到了上述边值问题正解的存在性.

Consider the boundary value problem of delta-nabla fractional difference equations with p-Laplacian operator: ■ Where b∈Z+, T=[α-β-1,b+α-β-1]Να-β-1, 1≤α,β≤2, 3<α+β≤4, 0<ω<1, λ∈(0,+∞), Δ■, b?α are left and right fractional difference operator, and ■. By using the upper and lower solution method and the Schauder fixed point theorem, the existence of the positive solution of the above boundary value problem is obtained.