LAUSR

Abstract In this paper, we investigate nonlinear Hamiltonian elliptic system { ( - Δ ) u = b → ( x ) ⋅ ∇ u + ( V ( x ) + τ ) u = K ( x ) g ( v ) in ℝ ℕ , ( - Δ ) v = b → ( x ) ⋅ ∇ v + ( V ( x ) + τ ) v = K ( x ) f ( u ) in ℝ ℕ , u ( x ) → 0 a n d v ( x ) → 0 a s | x | → ∞ , where N ≥ 3, τ > 0 is a positive parameter and V, K are nonnegative continuous functions, f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing a variational setting, the existence of ground state solutions is obtained.