Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
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 fo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/1565731 |
| Summary: | 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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| ISSN: | 1687-9120 1687-9139 |