DONG Qiang,HOU Chengmin*.Existence of positive solutions for p -Laplacian fractional differenceinvolving the discrete delta-nabla fractional boundary value problem[J].Journal of Yanbian University,2019,45(04):283-291.
具有p -Laplacian算子的delta-nabla分数阶 差分边值问题正解的存在性
- Title:
- Existence of positive solutions for p -Laplacian fractional difference involving the discrete delta-nabla fractional boundary value problem
- 文章编号:
- 1004-4353(2019)04-0283-09
- 关键词:
- delta-nabla分数阶差分; 边值问题; 上解和下解; Schauder不动点定理; p -Laplacian算子
- Keywords:
- delta -nabla fractional difference; boundary value problem; upper solution and lower solution; Schauder fixed point theorem; p -Laplacian operator
- 分类号:
- O175.8
- 文献标志码:
- A
- 摘要:
- 考虑具有p -Laplacian算子的delta -nabla分数阶差分方程边值问题: {Δβα -2(φp(b▽αx(t)))+λ f(t-α+β+1,x(t-α+β+1),[b▽εx(t)]t -α +β + ε +1)=0, t∈T; x(b)=0, b -1▽α -1x(α-2)=[b +α -2▽-ωg(t,x(t))]t =α -ω -1; [b▽αx(t)]α -2=0, [b▽αx(t)]α + b -2=0. 其中b∈Z+, T=[α-β-1,b+α-β-1]Ν<sup>α -β -1, 1≤α, β≤2, 3<α+β≤4, 0<ω<1, λ∈(0,+∞), Δβα -2和 b▽α分别是左右分数阶差分算子,并且φp(s)=|s|p -2s, p>1.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.
- Abstract:
- Consider the boundary value problem of delta-nabla fractional difference equations with p -Laplacian operator: {Δβα -2(φp(b▽αx(t)))+λ f(t-α+β+1,x(t-α+β+1),[b▽εx(t)]t -α +β + ε +1)=0, t∈T; x(b)=0, b -1▽α -1x(α-2)=[b +α -2▽-ωg(t,x(t))]t =α -ω -1; [b▽αx(t)]α -2=0, [b▽αx(t)]α +b -2=0. Where b∈Z+, T=[α-β-1,b+α-β-1]Ν<sup>α -β -1, 1≤α,β≤2, 3<α+β≤4, 0<ω<1, λ∈(0,+∞), Δβα -2, b▽α are left and right fractional difference operator, and φp(s)=|s|p -2s, p>1. 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.
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备注/Memo
收稿日期: 2019-09-21
*通信作者: 侯成敏(1963—),女,教授,研究方向为微分方程理论及其应用.