带p-Laplacian算子的分数阶微分方程的正解

Positive solutions for fractional differential equation with a p-Laplacian operator

研究一类带p-Laplacian算子的高阶多点Caputo分数阶微分方程:Dβ0+(φp(Dα0+u(t)))+f(t,u(t))=0,0≤t≤1,l-1<β≤l,n-1<α≤n,(φp(Dα0+u(0)))(i)=0,i=0,1,2,…,l-1,■m-2u(i)(0)=0,i=1,2,…,n-1,u(1)=∑aiu(ξi)。■i=1运用Schauder不动点定理,得到边值问题正解的存在性,最后给出了例子来验证所得结论。

This paper studies the following Caputo fractional differential equation with p-Laplacian of higher-order multi-point：Dβ0＋（φp（Dα0＋u（t）））＋f（t,u（t））=0, 0≤t≤1,l-1β≤l,n-1α≤n,■（φp（Dα0＋u（0）））（i）=0, i=0,1,2,…,l-1,■m-2■u（i）（0）=0, i=1,2,…,n-1, u（1）=∑aiu（ξi）。i=1Using the Schauder fixed point theorem,the existence of positive solution is obtained for the above boundary value problems.An example is presented to illustrate our main theorem.