PROPERTIES OF THE POSITIVE SOLUTIONS OF FRACTIONAL P&Q-LAPLACE EQUATIONS WITH A SIGN-CHANGING POTENTIAL  

作　　者：Yubo DUAN Yawei WEI 段雨博;魏雅薇(School of Mathematical Sciences,Nankai University,Tianjin 300071,China;School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China)

机构地区：[1]School of Mathematical Sciences,Nankai University,Tianjin 300071,China [2]School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China

出　　处：《Acta Mathematica Scientia》2024年第6期2422-2442,共21页数学物理学报（B辑英文版）

基　　金：partially supported by the NSFC(12271269);the Fundamental Research Funds for the Central Universities;partially supported by the Fundamental Research Funds for the Central Universities(2021YJSB006)。

摘　　要：In this paper,we consider the nonlinear equations involving the fractional p&qLaplace operator with a sign-changing potential.This model is inspired by the De Giorgi Conjecture.There are two main results in this paper.First,in the bounded domain,we use the moving plane method to show that the solution is radially symmetric.Second,for the unbounded domain,in view of the idea of the sliding method,we find the existence of the maximizing sequence of the bounded solution,then obtain that the solution is strictly monotone increasing in some direction.

关 键 词：fractional p&q-Laplacian moving plane method sliding method 

分 类 号：O175[理学—数学]