Symmetry and regularity of solutions to a system with three-component integral equations |
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Authors: | ChangZheng Qu JingBo Dou |
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Institution: | 1Department of Mathematics,Ningbo University,Ningbo 315211,China;2School of Statistics,Xi’an University of Finance and Economics,Xi’an 710100,China |
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Abstract: | Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < n,n is a positive constant,p,q and r satisfy some suitable conditions.It is shown that every positive regular solution(u(x),v(x),w(x)) is radially symmetric and monotonic about some point by developing the moving plane method in an integral form.In addition,the regularity of the solutions is also proved by the contraction mapping principle.The conformal invariant property of the system is also investigated. |
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Keywords: | system of integral equations symmetry regularity conformal invariance |
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