Existence of positive solutions to nonlinear elliptic systems involving gradient term and reaction potential
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In 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.
CitationAttar, A., & Bentifour, R. (2017). Existence of positive solutions to nonlinear elliptic systems involving gradient term and reaction potential. Electronic Journal of Differential Equations, 2017(113), pp. 1-10.
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