Xue Xiu ZHONG, Wen Ming ZOU
Consider the Schrödinger system
where Ω ⊂ R
N,
α,
β > 1,
α +
β < 2* and the spectrum σ(-Δ+
Vi,n) ⊂ (0,+∞),
em = 1, 2;
Qn is a bounded function and is positive in a region contained in Ω and negative outside. Moreover, the sets {
Qn > 0} shrink to a point
x0 ∈ Ω as
n→ +∞. We obtain the concentration phenomenon. Precisely, we first show that the system has a nontrivial solution (
un,
vn) corresponding to
Qn, then we prove that the sequences (
un) and (
vn) concentrate at
x0 with respect to the H1-norm. Moreover, if the sets {
Qn> 0} shrink to finite points and (
un,
vn) is a ground state solution, then we must have that both
un and
vn concentrate at exactly one of these points. Surprisingly, the concentration of
un and
vn occurs at the same point. Hence, we generalize the results due to Ackermann and Szulkin [Arch. Rational Mech. Anal., 207, 1075-1089 (2013)].
-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W, where 
