Classification of Positive Solitary Solutions of the Nonlinear Choquard Equation

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Singularly perturbed critical Choquard equations (2016, methodology): “Recently, by using the method of moving planes, Ma and Zhao [22] proved that all the positive solutions of equation (1.4) must be radially symmetric and monotone decreasing about some fixed point.”
Uniqueness of Radial Solutions for the Fractional Laplacian (2013, methodology): “Hence we conclude from the moving plane arguments in [31] that Q.”
Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity (2018, methodology): “Inspired by [24, 27, 28], we introduce the following basic assumption on f : (F1) f ∈ C(R,R), f(t) = o(|t|α/3) as |t|→ 0 and f(t) = o(|t|2+α) as |t|→∞.”
Uniqueness of non-linear ground states for fractional Laplacians in $${\mathbb{R}}$$R (2010, methodology): “3 with the slightly weaker statement that Q̃(r) is (not necessarily strictly) decreasing, we can directly apply the moving plane arguments developed in [24].”
Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains (2012, methodology): “studied the symmetry of positive radial ground state of (C) with constant V in higher dimensions using the moving–plane method [24].”