Multiplicity results of fractional-Laplace system with sign-changing and singular nonlinearity
Date
2017-07-18
Authors
Goyal, Sarika
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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).
Description
Keywords
Fractional-Laplacian system, Singular nonlinearity, Sign-changing weight function
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.
Rights
Attribution 4.0 International