%0 Journal Article %J Ann. of Math. 168 (2008) 813-858 %D 2008 %T Existence of conformal metrics with constant $Q$-curvature %A Zindine Djadli %A Andrea Malchiodi %X 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. %B Ann. of Math. 168 (2008) 813-858 %G en_US %U http://hdl.handle.net/1963/2308 %1 1708 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-29T14:05:55Z\\nNo. of bitstreams: 1\\nDjadliMalchiodiFinal.pdf: 342979 bytes, checksum: fc2b0b8e4e01a5327ed8e01dc1bae6c5 (MD5)