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Electronic Journal of Differential Equations
We study the following quasilinear problem with nonlinear boundary conditions −∆pu = λa(x)|u| p−2 u + k(x)|u| q−2 u − h(x)|u| s−2 u, in Ω, ||u| p−2 u · η + b(x)|u| p−2 u = 0 on ∂Ω, where Ω is an unbounded domain in R N with a noncompact and smooth boundary ∂Ω, η denotes the unit outward normal vector on ∂Ω, ∆pu = div(||u| p−2 u) is the p-Laplacian, a, k, h and b are nonnegative essentially bounded functions, q < p < s and p * < s. The properties of the first eigen-value λ 1 and the associatedfatcat:uizlkln7ljblrpabges2j47iaq