MULTIPLE POSITIVE SOLUTIONS TO A CLASS OF MODIFIED NONLINEAR SCHR?DINGER EQUATION IN A HIGH DIMENSION  

作　　者：钟延生 李永青 Yansheng ZHONG;Yongqing LI(School of Mathematics and Statistics&FJKLMAA,&Center for Applied Mathematics of Fujian Province(FJNU),Fujian Normal University,Fuzhou 350117,China)

机构地区：[1]School of Mathematics and Statistics&FJKLMAA,&Center for Applied Mathematics of Fujian Province(FJNU),Fujian Normal University,Fuzhou 350117,China

出　　处：《Acta Mathematica Scientia》2023年第4期1819-1840,共22页数学物理学报（B辑英文版）

基　　金：Partially the NSFC(11671085);the Science Foundation of Fujian Province(2020J01160)。

摘　　要：The existence and multiplicity of positive solutions for equation(1.1)with the new critical exponent 4<p<2·2*shall be investigated in a high dimension.The conclusions extend the relative results recently attained in[1]for the one-dimensional case.More precisely,as the coefficient a(x)in the nonlinearity is sign-changing,the modified term 2(Δ(|u|2))u is still helpful for obtaining multiple positive solutions in a high dimension,even if a sign condition like∫_(R)N a(x)e_(1)^(p)dx<0(also named“a necessary condition”see[2,3])does not hold.

关 键 词：variational methods nonlinear Schrodinger equation sign-changing 

分 类 号：O175.2[理学—数学]