A COMPACT EMBEDDING RESULT FOR NONLOCAL SOBOLEV SPACES AND MULTIPLICITY OF SIGN-CHANGING SOLUTIONS FOR NONLOCAL SCHRÖDINGER EQUATIONS  

作　　者：Xu ZHANG Hao ZHAI Fukun ZHAO 张徐;翟昊;赵富坤(Department of Mathematics,Wuhan University of Technology,Wuhan,430070,China;Department of Mathematics,Yunnan Normal University,Kunming,650500,China)

机构地区：[1]Department of Mathematics,Wuhan University of Technology,Wuhan,430070,China [2]Department of Mathematics,Yunnan Normal University,Kunming,650500,China

出　　处：《Acta Mathematica Scientia》2024年第5期1853-1876,共24页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(12261107);Yunnan Key Laboratory of Modern Analytical Mathematics and Applications(202302AN360007).

摘　　要：For any s∈(0,1),let the nonlocal Sobolev space X^(s)(R^(N))be the linear space of Lebesgue measure functions from R^(N) to R such that any function u in X^(s)(R^(N))belongs to L2(R^(N))and the function(x,y)→(u(x)-u(y)√K(x-y)is in L^(2)(R^(N),R^(N)).First,we show,for a coercive function V(x),the subspace E:={u∈X^s(R^N):f_(R)^N}V(x)u^(2)dx<+∞}of X^(s)(R^(N))is embedded compactly into L^(p)(R^(N))for p\in[2,2_(s)^(*)),where 2_(s)^(*)is the fractional Sobolev critical exponent.In terms of applications,the existence of a least energy sign-changing solution and infinitely many sign-changing solutions of the nonlocal Schrödinger equation-L_(k)u+V(x)u=f(x,u),x∈R^N are obtained,where-L_(K)is an integro-differential operator and V is coercive at infinity.

关 键 词：sign-changing solution integro-differential operator least energy variational method 

分 类 号：O175.2[理学—数学]