具有临界指数的k-耦合薛定谔系统的基态解

The least energy solution for k-coupled Schr?dinger equations with critical exponent

考虑 k-耦合薛定谔系统(P){-Δu j+λ ju j=∑^k i=1 β ji u ju^ 2 i , x∈Ω u j=0 , j=1,2,…,k, x∈■Ω证明了在系数满足一定条件时正的基态解的存在性以及非平凡解的不存在性结果。

Consider the k -coupled Schr dinger system:(P){-Δu j+λ ju j=∑^k i=1 β ji u ju^ 2 i , x∈Ω u j=0 , j=1,2,…,k, x∈■Ω It proves the existence of positive least energy solution of system (P) and the non-existence of the nontrivial solution of system (P) when the coefficient meet certain conditions.