EXISTENCE OF SOLUTIONS FOR THE FRACTIONAL(p,q)-LAPLACIAN PROBLEMS INVOLVING A CRITICAL SOBOLEV EXPONENT  

作　　者：Fanfan CHEN Yang YANG 陈帆帆;杨阳(School of Science,Jiangnan University,Wuxi 214122,China)

机构地区：[1]School of Science,Jiangnan University,Wuxi 214122,China

出　　处：《Acta Mathematica Scientia》2020年第6期1666-1678,共13页数学物理学报（B辑英文版）

基　　金：National Natural Science Foundation of China(11501252 and 11571176)。

摘　　要：In this article,we study the following fractional(p,q)-Laplacian equations involving the critical Sobolev exponent:(Pμ,λ){(−Δ)s 1 p u+(−Δ)s 2 q u=μ|u|q−2 u+λ|u|p−2 u+|u|p∗s 1−2 u,u=0,inΩ,in R N∖Ω,whereΩ⊂R N is a smooth and bounded domain,λ,μ>0,0<s 2<s 1<1,1<q<p<Ns 1.We establish the existence of a non-negative nontrivial weak solution to(Pμ,λ)by using the Mountain Pass Theorem.The lack of compactness associated with problems involving critical Sobolev exponents is overcome by working with certain asymptotic estimates for minimizers.

关 键 词：fractional(p q)-Laplacian non-negative solutions critical Sobolev exponents 

分 类 号：O175[理学—数学]