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

Linfen Cao, Xiaoshan Wang and Zhaohui Dai

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

Abstract: 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 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.

Date: 2018
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https://doi.org/10.1155/2018/1565731

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:1565731

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