@article {2008, title = {Existence of conformal metrics with constant $Q$-curvature}, journal = {Ann. of Math. 168 (2008) 813-858}, number = {SISSA;70/2004/M}, year = {2008}, abstract = {Given 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.}, url = {http://hdl.handle.net/1963/2308}, author = {Zindine Djadli and Andrea Malchiodi} }