【摘要】 利用变分方法和临界点理论讨论了一类带有分数阶p-拉普拉斯算子的Schr?dinger-rKirchhoff方程多重解的存在性M(∫∫_R^2N|u（x）-u（y）|^p/|x-y|^N+psdxdy)（-Δ）_p^s u+V（x）|u|^p-2u=f（x,u）+λh（x）|u|^r-2u,x∈R^N,其中λ∈R,0 <s <1 <r <p <2,ps <N,（-△）_p^s表示分数阶p-拉普拉斯算子.首先,利用对称山路定理得到该方程无穷多高能量解的存在性.其次,利用对偶喷泉定理证明了上述方程有一列趋于0的负能量解.更多还原

【Abstract】 In this article,we use variational method and the critical point theory to study the existence of multiple solutions for a class of Schrodinger-Kirchhoff equation involving the fractional p-Laplacian operator M(∫∫_{R^{2 N}} |u（x）-u（y）|^p/|x-y|^N+psdxdy)（-Δ）_p^s u+V（x）|u|^p-2u=f（x,u）+λh（x）|u|^r-2u,x∈R^N,where λ ∈ R,0 <s <1<r <p <2,ps <N,（-Δ）_p^s is the fractional p-Laplacian operator.Under certain assumptions,we first show the existence of multiple high energy solutions by means of symmetric mountain pass theorem.Secondly,by using dual fountain theorem,we prove that the above equation has a sequence of negative energy solution,whose energy converges to0.更多还原