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Nonlinear elliptic systems with coupled gradient terms

Abstract : In this paper, we analyze the existence and non-existence of nonnegative solutions to a class of nonlinear elliptic systems of type : −∆u = |∇v| q + λf in Ω, −∆v = |∇u| p + µg in Ω, u = v = 0 on ∂Ω, u, v ≥ 0 in Ω, where Ω is a bounded domain of IR N and p, q ≥ 1. f, g are nonnegative measurable functions with additional hypotheses and λ, µ ≥ 0. This extends previous similar results obtained in the case where the right-hand sides are potential and gradient terms, see [2, 4].
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Submitted on : Thursday, July 1, 2021 - 2:41:48 PM
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Ahmed Attar, Rachid Bentifour, El-Haj Laamri. Nonlinear elliptic systems with coupled gradient terms. Acta Applicandae Mathematicae, Springer Verlag, 2020, 170 (1), pp.163-183. ⟨10.1007/s10440-020-00329-7⟩. ⟨hal-03275893⟩



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