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

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  • Linfen Cao
  • Xiaoshan Wang
  • Zhaohui Dai

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 , if and satisfy the following nonlinear system and are nonnegative continuous functions satisfying the following: (i) and are increasing for ; (ii) , are bounded near . Then the positive solutions must be radially symmetric and monotone decreasing about the origin.

Suggested Citation

  • Linfen Cao & Xiaoshan Wang & Zhaohui Dai, 2018. "Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-6, August.
    • Handle: RePEc:hin:jnlamp:1565731
    DOI: 10.1155/2018/1565731
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