Jleli, MohamedSamet, Bessem2022-04-112022-04-112017-04-18Jleli, M., & Samet, B. (2017). Liouville-type theorems for an elliptic system involving fractional Laplacian operators with mixed order. <i>Electronic Journal of Differential Equations, 2017</i>(105), pp. 1-11.1072-6691https://hdl.handle.net/10877/15637We study the nonexistence of nontrivial solutions for the nonlinear elliptic system Gα, β, θ(up, uq) = vr Gλ, μ, θ(vs, vt) = um u, v ≥ 0, where 0 < α, β, λ, μ ≤ 2, θ ≥ 0, m > q ≥ p ≥ 1, r > t ≥ s ≥ 1, and Gα, β, θ is the fractional operator of mixed orders α, β, defined by Gα, β, θ(u, v) = (-∆x)α/2u + |x|2 θ (-∆y)β/2v, in ℝN1 x ℝN2. Here, (-∆x)α/2, 0 < α < 2, is the fractional Laplacian operator of order α/2 with respect to the variable x ∈ ℝN1, and (-∆y)β/2, 0 < β < 2, is the fractional Laplacian operator of order β/2 with respect to the variable y ∈ ℝN2. Via a weak formulation approach, sufficient conditions are provided in terms of space dimension and system parameters.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalLiouville-type theoremNonexistenceFractional Grushin operatorArticle