Liouville-type theorems for an elliptic system involving fractional Laplacian operators with mixed order
| dc.contributor.author | Jleli, Mohamed | |
| dc.contributor.author | Samet, Bessem | |
| dc.date.accessioned | 2022-04-11T19:45:54Z | |
| dc.date.available | 2022-04-11T19:45:54Z | |
| dc.date.issued | 2017-04-18 | |
| dc.description.abstract | We 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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 11 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Jleli, 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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15637 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Liouville-type theorem | |
| dc.subject | Nonexistence | |
| dc.subject | Fractional Grushin operator | |
| dc.title | Liouville-type theorems for an elliptic system involving fractional Laplacian operators with mixed order | |
| dc.type | Article |