The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE (Q1969239)

The Paneitz operator \(P\), a conformally invariant differential operator of order four on a compact four-dimensional Riemannian manifold is studied. In terms of conformal invariants of the manifold a sufficient criterion is given under which the principal eigenvalue \(\lambda_1(P)=0.\) If the Yamabe invariant is positive, there is an upper bound for another conformal invariant \(\kappa_g,\) in the case of equality the manifold is conformally equivalent to the standard sphere.