Infinitely many solutions to elliptic systems with critical exponents and Hardy potentials

In this paper, we consider the following elliptic systems with critical Sobolev growth and Hardy potentials: where N ≥ 3, η > 0, λ₁,λ₂ ∈ [0,Λ_N), and is the best Hardy constant. is the critical Sobolev exponent. a₁, a₂, b₁, and b₂ are positive parameters, and α,β > 1 satisfy 2 < α + β < 2*. h(x) ? 0, h(x) ≥ 0, , , and with . By means of the concentration–compactness principle and R. Kajikiya's new version of symmetric mountain pass lemma, we obtain infinitely many solutions that tend to zero. Copyright © 2013 John Wiley & Sons, Ltd.