Nonlinear elliptic systems with coupled gradient terms
Résumé
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].
Domaines
Mathématiques [math]
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