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In this article we study the nonlinear Robin boundary-value problem - Δ p ( x ) u = f ( x , u ) i n Ω , | ∇ u | p x - 2 ( ∂ u / ∂ ν ) + β ( x ) u p ( x ) - 2 u = 0 on ∂ Ω . Using the variational method, under appropriate assumptions on f , we obtain results on existence and multiplicity of solutions.

Existence of Solutions for a Robin Problem Involving the p ( x ) -Laplace Operator