Liouville type theorems for the system of fractional nonlinear equations in R + n ${R^{n}_{+}}$

Dai, Zhaohui; Cao, Linfen; Wang, Pengyan

doi:10.1186/s13660-016-1207-9

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…The fractional and nonlocal operators of elliptic type due to concrete real world have been applied in finance, thin obstacle problem, optimization, quasi-geostrophic flow, etc. In recent years, there have been tremendous interests in developing the problems related to fractional Laplacian (see in [1][2][3][4][5] and the reference therein). Fractional p-Laplacian is a generalization of the fractional Laplacian, but there are few interesting results about these nonlinear equations involving fractional p-Laplacian.…”

Section: Introductionmentioning

confidence: 99%

Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

Cao

Wang

Dai

2018

Advances in Mathematical Physics

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In this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For 0<s,t<1,p>0, if u and v satisfy the following nonlinear system -Δpsux=fvx; -Δptvx=gux, x∈B10; ux,vx=0, x∉B10. and f,g are nonnegative continuous functions satisfying the following: (i) f(r) and g(r) are increasing for r>0; (ii) f′(r)/rp-2, g′(r)/rp-2 are bounded near r=0. Then the positive solutions (u,v) must be radially symmetric and monotone decreasing about the origin.

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Section: Introductionmentioning

confidence: 99%

Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

Cao

Wang

Dai

2018

Advances in Mathematical Physics

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“…Introduction. In recent years, the fractional Laplace equations have been frequently used to describe many science phenomena, such as the turbulence, water waves, anomalous diffusion and quasi-geostrophic flows (see [7], [16], [17], [33] and the references therein). It also has various applications in probability and finance (see [3], [5]).…”

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confidence: 99%

Liouville's theorem for a fractional elliptic system

Wang¹,

Niu²

2019

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper, we investigate the following fractional elliptic system (−) α/2 u(x) = f (x)v q (x), x ∈ R n , (−) β/2 v(x) = h(x)u p (x), x ∈ R n , where 1 ≤ p, q < ∞, 0 < α, β < 2, f (x) and h(x) satisfy suitable conditions. Applying the method of moving planes, we prove monotonicity without any decay assumption at infinity. Furthermore, if α = β, a Liouville theorem is established.

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Symmetry and monotonicity of positive solutions for a system involving fractional p&q-Laplacian in a ball

Cao

Fan

2021

Complex Variables and Elliptic Equations

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Liouville type theorems for the system of fractional nonlinear equations in R + n ${R^{n}_{+}}$

Abstract: In this paper we consider the following system of fractional nonlinear equations in the half space R

Cited by 3 publications

References 6 publications

Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

Liouville's theorem for a fractional elliptic system

Symmetry and monotonicity of positive solutions for a system involving fractional p&q-Laplacian in a ball

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