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In [11, 12], the authors introduced a method of plane parqueting, which can be used to determine a Schwarz operator, the harmonic Green and Neumann functions, and requires that reflecting the domain at all of these circular or straight curves produces a parqueting of whole complex plane with possible exception of singular points.
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By the method of moving plane in integral form, Jin and Li in [5] showed that all of the positive solutions of (1.7) are radially symmetric.
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To obtain our results, in this section, we will use the method of moving plane in the integral forms recently introduced by Chen et al. in [13] and prove the radial symmetry and monotonicity of positive solutions of system (1.1).
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Part 2. The method of moving planes.
Now we introduce some basic notations in the method of moving planes.
To this end, we employ a certain type of Kelvin transform and the method of moving planes in integral forms.
Using the method of moving planes, we show that any parabolically convex solution is symmetric with respect to some hyperplane.
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