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 Existence and Multiplicity of solutions for a quasilinear elliptic system on unbounded domains involving nonlinear boundary conditions Somayeh Khademloo,Ghasem Alizadeh Afrouzi,Jiafa Xu Keywords:Quasilinear elliptic systems, Nonlinear boundary conditions, Variational methods, Weighted function spaces Abstract: We prove several existence results for the nonlinear elliptic boundary value system involving $p$-Laplacian over an unbounded domain in $R^N$ with noncompact boundary. The proofs are based on variational methods applied to weighted spaces.