## Periodic Hamiltonian elliptic systems in unbounded domains |

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ae(A Assume by contradiction assumptions of Lemma asymptotically quadratic attractor bounded set C)/-attractor Campinas Cauchy problem compact continuous with respect critical values define denote elliptic equations embedded essential spectrum Examples which satisfies existence f H(x,zj f(zj Fibonacci Figueiredo finite dimensional subspace finite r-open refinement finite set Francisco function Furtado Hamiltonean Elliptic Systems hence holds Hz(x implies infinitely many geometrically let zj Lie group lim sup liminf Marcelo F Marko max V)2 Metric Spaces multiplicity Nonlinearity norm topologies Number oc uniformly Optimal Control order to show partition of unity prove pseudo-gradient vector field Qj(r Quasilinear r-Lipschitz continuous partition r-open neighborhood r-topology remain true Rojas-Medar Ronaldo Dias set Wj Sobolev space standard argument shows symmetric symplectic representation system HS Theorem 1.1 tion with Symmetry unbounded domains unity subordinated variational setting weakly sequentially continuous weakly sequentially lower zj(x