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In this paper, we obtain some new results on the existence of non-negative solutions for systems of the form where each of the q i are positive potentials satisfying lim |x|→+∞ q i (x) = +∞, each of the m i are bounded positive weights, each of the a ij , i = j, are bounded non-negative weights and each of the µ i are real parameters. Depending upon the(More)
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)
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