Existence of Conformal Metrics with Prescribed Q-Curvature

Abstract

We consider the problem of existence of conformal metrics with prescribed Q-curvature on standard sphere , ≥ 5. Under the assumption that the order of flatness at critical points of prescribed Q-curvature function ( ) is ∈ ]1, − 4], we give precise estimates on the losses of the compactness, and we prove new existence and multiplicity results through an Euler-Hopf type formula.

Q-curvature type problem on bounded domains of R n

“…The latter has widely studied in the last two decades. (See [2] [12], [6], [7], [3], [10], [11], [15], [16], [17] and the references therein for details). Problem (1.1) has a variational structure with challenging mathematical difficulties.…”