This paper is concerned with the following periodic Hamiltonian elliptic system: ? Δ u + V ( x ) u = H v ( x , u , v ) , x ∈ R N , ? Δ v + V ( x ) v = H u ( x , u , v ) , x ∈ R N , u ( x ) → 0 , v ( x ) → 0 as | x | → ∞ . Assuming the potential V is periodic and 0 lies in a gap of σ ( ? Δ + V ) , H ( x , z ) is periodic in x and superquadratic in z = ( u , v ) . We establish the existence of infinitely many large energy solutions by the generalized variant fountain theorem developed recently by Batkam and Colin. MSC: 35J50, 35J55.
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机译：本文涉及以下周期性哈密顿椭圆系统： Δu + V（x）u = H v（x，u，v），x∈R N，？ Δv + V（x）v = H u（x，u，v），x∈R N，u（x）→0，v（x）→0为| x | →∞。假设电势V是周期性的，并且0位于σ（？Δ+ V）的间隙中，则H（x，z）在x中是周期性的，在z =（u，v）中是超二次的。通过Batkam和Colin最近开发的广义变体喷泉定理，我们建立了无限多个大型能量解的存在。 MSC：35J50、35J55。
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