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In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form −div(h(x)|∇u| p−2 ∇u) + b(x)|u| p−2 u = f (x, u), p ≥ 2 in an unbounded domain Ω ⊂ R N , N ≥ 3, with sufficiently smooth bounded boundary ∂Ω, where h(x) ∈ L 1 loc (Ω), Ω = Ω ∪ ∂Ω, h(x) ≥ 1 for all x ∈ Ω. The proof of main… (More)

This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form{(-div (h 1 (x) u) = λ F u (x, u, v), in Ω,;-div (h 2 (x) v) = λ F v (x, u, v), in Ω,) where Ω is a bounded domain with smooth boundary ∂Ω in R N , N 2, and h i : Ω → [0, ∞), h i L loc 1 (Ω), h i (i =… (More)

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