【摘要】 研究了一类分数阶p-Laplacian方程（-Δ）_p^su+V（x）|u|^p-2u=f（x,u）,x∈R^N弱解的存在性问题.其中:p≥2;N≥2;s∈（0,1）;V（x）∈C（RN）是变号的势函数;（-Δ）sp是分数阶p-Laplacian算子;非线性项f:RN×R→R是Carathéodory泛函.运用山路引理,建立了该方程非平凡弱解的存在性定理.更多还原

【Abstract】 It was studied to the existence of solutions of the following nonlocal fractional p-Laplacian equation （-Δ）_p^su+V（x）|u|^p-2u=f（x,u）,x∈R^N.where p≥2,N≥2 and s∈（0,1）,V（x） ∈C（R^N） was a function possibly changing sign,（-Δ）spdenoted the fractional p-Laplacian and nonlinearity f: R^N× R → R was a Carathéodory function. By using mountain pass theorem,the existence theorem of the week solutions for the equation was established.更多还原