For the Schrodinger system{-△uj+λjuj+k∑i=1βijui^2uj in R^N,uj(x)→0 as|x|→∞,j=1,…,k where k≥2 and N=2,3,we prove that for anyλj>0 andβjj>0 and any positive integers pj,j=1,2,…,k,there exists b>0 su...For the Schrodinger system{-△uj+λjuj+k∑i=1βijui^2uj in R^N,uj(x)→0 as|x|→∞,j=1,…,k where k≥2 and N=2,3,we prove that for anyλj>0 andβjj>0 and any positive integers pj,j=1,2,…,k,there exists b>0 such that ifβij=βji≤b for all i≠j then there exists a radial solution(u1,u2,…uk)with uj having exactly Pj-1 zeroes.Moreover,there exists a positive constant Co such that ifβij=βji≤b(i≠j)then any solution obtained satisfies k∑i,j=1|βij|∫R^Nui^2uj^2≤C0.Therefore,the solutions exhibit a trend of phase separations asβij→-∞for i≠j.展开更多
基金supported by the National Natural Science Foundation of China with grand numbers Nos.11671272,11331010,11771324 and 11831009
文摘For the Schrodinger system{-△uj+λjuj+k∑i=1βijui^2uj in R^N,uj(x)→0 as|x|→∞,j=1,…,k where k≥2 and N=2,3,we prove that for anyλj>0 andβjj>0 and any positive integers pj,j=1,2,…,k,there exists b>0 such that ifβij=βji≤b for all i≠j then there exists a radial solution(u1,u2,…uk)with uj having exactly Pj-1 zeroes.Moreover,there exists a positive constant Co such that ifβij=βji≤b(i≠j)then any solution obtained satisfies k∑i,j=1|βij|∫R^Nui^2uj^2≤C0.Therefore,the solutions exhibit a trend of phase separations asβij→-∞for i≠j.
