Positive Solutions for a Class of Fractional p-Laplacian Equation with Critical Sobolev Exponent and Decaying Potentials  

作　　者：Na LI Xiao-ming HE 

机构地区：[1]College of Science,Minzu University of China,Beijing 100081,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第2期463-483,共21页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12171497,11771468,11971027)。

摘　　要：In this paper,we study the existence of positive solution for the p-Laplacian equations with frac-tional critical nonlinearity{-Δ)_(p)^(s)u+V(x)|u|^(p-2)u=K(x)f(u)+P(x)|u|p_(s)^(*)-^(2)u,x∈R^(N),u∈Ds,p(RN),where s∈(0,1),p_(s)^(*)=Np/N-sp,N>sp,p>1 and V(x),K(x)are positive continuous functions which vanish at infinity,f is a function with a subcritical growth,and P(x)is bounded,nonnegative continuous function.By using variational method in the weighted spaces,we prove the above problem has at least one positive solution.

关 键 词：Fractional p-Laplacian Variational methods Mountain Pass Theorem Critical growth Vanishing potential 

分 类 号：O175[理学—数学]