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where Ω ⊆ R is an unbounded domain with noncompact smooth boundary ∂Ω, the outward unit normal to which is denoted by n with p > 1 and i = 1, ..., n. The growing attention for the study of the p-Laplacian operator in the last few decades is motivated by the fact that it arises in various applications. The p-Laplacian operator in (1.1) is a special case of the divergence form operator −div(a(x,∇u)), which appears in many nonlinear diffusion problems, in particular in the mathematical modeling of non-Newtonian fluids, for a discussion of some physical background, see [9]. We also refer to Aronsson-Janfalk [1] for the

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A QUASILINEAR ELLIPTIC SYSTEM ON UNBOUNDED DOMAINS INVOLVING NONLINEAR BOUNDARY CONDITIONS