Classification of positive smooth solutions to third-order PDEs involving fractional Laplacians (Q1744256)

This authors study a third-order conformal invariant equation with critical nonlinearity and a third-order critical static Hartree equation with nonlocal nonlinearity. By showing the equivalence between PDE and a integral equation, using some results in [\textit{W. Chen} et al., Commun. Pure Appl. Math. 59, No. 3, 330--343 (2006; Zbl 1093.45001)], the authors establish the classification of positive smooth solutions to the third-ordor equation under assumptions which are similar to or weaker than those in some relative references.