We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the ...We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.展开更多
基金supportedby the National Natural Science Foundation of China(Grant No.11971393).
文摘We study the Schrodinger-KdV system{-△u+λ1(x)u=u^3+βuv,u∈H^1(R^N),-△v+λ2(x)v=1/2v^2+β/2u^2,v∈H^1(R^N),where N=1,2,3,λi(x)∈C(R^N,R),lim|x|→∞λi(x)=λi(∞),and λi(x)≤λi(∞),i=1,2,a.e.x∈R^N.We obtain the existence of nontrivial ground state solutions for the above system by variational methods and the Nehari manifold.
