中文摘要：

研究一类带有临界指数的分数阶p-Laplacian方程（-Δ）spu＋V（x）up-2u=up＊s-2u＋f（x,u）,x∈N,弱解的存在性问题,其中p≥2,N≥2,N〉ps,p＊s=Np/（N-ps）,s∈（0,1）,（-Δ）sp是分数阶p-Laplacian算子,非线性项f∶N×→是Carathéodory泛函。运用山路引理,建立了该方程弱解的存在性定理。

英文摘要：

In this paper, we study the existence of week solutions for the following fractional p-Laplacian equation with critical exponent （-Δ）spu＋V（x）up-2u=up＊s-2u＋f（x,u）,x∈N,where p≥2,N≥2,N〉ps,p＊s=Np/（N-ps）,s∈（0,1）,（-Δ）sp tands for the fractional p-Laplacian and nonlinearity f∶N×→K is a Carath6odory function. By using the mountain pass theorem,the existence theorem of the week solutions of the equation is established.