Abstract
This paper is concerned with the following nonperiodic Hamiltonian elliptic system {−Δu+V(x)u=Hv(x,u,v)−Δv+V(x)v=Hu(x,u,v)x∈RN,u(x),v(x)→0as|x|→∞, where z=(u,v):RN→R×R, N≥3. Assuming the potential V is nonperiodic and sign-changing, H(x,z) is nonperiodic in x and asymptotically quadratic in z=(u,v), existence and multiplicity of solutions are obtained via a variational approach.
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