Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry.

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The Paneitz equation in hyperbolic space (2008, background): “It is a simple but very useful observation that the initial value problem enjoys a comparison principle, see [25]: Lemma 1.”
Exact solutions of nonlinear conformally invariant integral equations in R 3 (2005, unknown): “Even for a radial case, the equation has already been difficult as one could see from recent work by McKenna and Reichel [17] which is based on our earlier work jointly with Choi [9].”
Remark on some conformally invariant integral equations: the method of moving spheres (2003, methodology): “Radial solutions of the biharmonic equations corresponding to (12) with n = 3 and p = 1 were studied by McKenna and Reichel in [34].”
Radial entire solutions for supercritical biharmonic equations (2006, methodology): “For this purpose we quote a comparison principle, which has been observed by McKenna-Reichel [9] and which will turn out to be useful also in the proof of uniqueness below: Lemma 2.”
Multiplicity of solutions for a fourth order equation with power-type nonlinearity (2010, background): “Problem (2) for positive powers has been studied in [5,14–16,31] and the case of negative powers has been treated in [9,11,16,26–28,34].”