Attar, AhmedBentifour, Rachid2022-04-132022-04-132017-04-26Attar, A., & Bentifour, R. (2017). Existence of positive solutions to nonlinear elliptic systems involving gradient term and reaction potential. <i>Electronic Journal of Differential Equations, 2017</i>(113), pp. 1-10.1072-6691https://hdl.handle.net/10877/15647In this note we study the elliptic system -∆u = zp + ƒ(x) in Ω, -∆z = |∇u|q + g(x) in Ω, z, u > 0 in Ω, z = u = 0 on ∂Ω, where Ω ⊂ ℝN is a bounded domain, p > 0, 0 < q ≤ 2 with pq < 1 and ƒ, g are two nonnegative measurable functions. The main result of this work is to analyze the interaction between the potential and the gradient terms in order to get the existence of a positive solution.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic systemSchauder fixed point theoremGradient dependenceArticle