POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM

doi:10.1016/S0252-9602(18)30794-X

Abstract

Abstract:

In this article, we study positive solutions to the system

To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.

Key words: Weighted fractional system, positive solution, radial symmetry, monotonicity, non-existence

Pengyan WANG, Yongzhong WANG. POSITIVE SOLUTIONS FOR A WEIGHTED FRACTIONAL SYSTEM[J].Acta mathematica scientia,Series B, 2018, 38(3): 935-949.

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