00797nas a2200109   4500008004300000245006300043210006000106520044300166100002000609700002200629856003600651       2008                        en_Ud  00aExistence of conformal metrics with constant $Q$-curvature0 aExistence of conformal metrics with constant Qcurvature3 aGiven a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and minimax schemes, jointly with a compactness result by the second author.1 aDjadli, Zindine1 aMalchiodi, Andrea  uhttp://hdl.handle.net/1963/2308