Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity
| dc.contributor.author | Goyal, Sarika | |
| dc.date.accessioned | 2022-06-08T19:09:59Z | |
| dc.date.available | 2022-06-08T19:09:59Z | |
| dc.date.issued | 2017-07-18 | |
| dc.description.abstract | In this article, we study the following fractional-Laplacian system with singular nonlinearity (-∆)s u = λƒ(x)u-q + α/α+β b(x)uα-1 wβ in Ω (-∆)s w = μg(x)w-q + β/α+β b(x)uα wβ-1 in Ω u, w > 0 in Ω, u = w = 0 in ℝn \ Ω, where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, n > 2s, s ∈ (0, 1), 0 < q < 1, α > 1, β > 1 satisfy 2 < α + β < 2*s - 1 with 2*s = 2n/n-2s, the pair of parameters (λ, μ) ∈ ℝ2 \ {(0, 0)}. The weight functions ƒ, g : Ω ⊂ ℝn → ℝ such that 0 < ƒ, g ∈ L α+β/α+β-1+q (Ω), and b : Ω ⊂ ℝn → ℝ is a sign-changing function such that b(x) ∈ L∞(Ω). Using variational methods, we show existence and multiplicity of positive solutions with respect to the pair of parameters (λ, μ). | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 28 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Goyal, S. (2017). Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity. Electronic Journal of Differential Equations, 2017(183), pp. 1-28. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15876 | |
| 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 | Fractional-Laplacian system | |
| dc.subject | Singular nonlinearity | |
| dc.subject | Sign-changing weight function | |
| dc.title | Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity | |
| dc.type | Article |