Existence results for the higher-order $Q$-curvature equation

Nonlinear higher-order PDEs (35G20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Higher-order elliptic equations (35J30) Variational methods for higher-order elliptic equations (35J35) Green's functions for elliptic equations (35J08) PDEs on manifolds (35R01) Conformal structures on manifolds (53C18)

Cites Work

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Explicit formulas for GJMS-operators and $Q$-curvatures
The $Q$-curvature on a 4-dimensional Riemannian manifold $(M,g)$ with $\int_M QdV_g = 8\pi^2$
GJMS-type operators on a compact Riemannian manifold: best constants and Coron-type solutions
A strong maximum principle for the Paneitz operator and a non-local flow for the $\mathcal Q$-curvature
A quartic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds (Summary)
Prescribed $Q$-curvature on manifolds of even dimension
Positive mass theorem for the Paneitz-Branson operator
Conformal deformation of a Riemannian metric to constant scalar curvature
Conformal metrics with prescribed scalar curvature
Conformally flat manifolds, Kleinian groups and scalar curvature
Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
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Conformal normal coordinates
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Paneitz-type operators and applications
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Existence of conformal metrics with constant $Q$-curvature
Remarks on GJMS operator of order six
Laplacian operators and $Q$-curvature on conformally Einstein manifolds
Riemannian manifolds with positive Yamabe invariant and Paneitz operator
Blow-up phenomena for the Yamabe equation
The Ambient Metric (AM-178)
Admissible $Q-$curvatures under isometries for the conformal GJMS operators
Q-Curvature on a Class of Manifolds with Dimension at Least 5
The Existence of Generalized Isothermal Coordinates for Higher Dimensional Riemannian Manifolds
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
Conformally Invariant Powers of the Laplacian, I: Existence
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Sign of Green's Function of Paneitz Operators and theQCurvature
Differential operators cononically associated to a conformal structure.
The Yamabe problem
Positive solutions for a fourth order equation invariant under isometries
Sharp Inequalities, the Functional Determinant, and the Complementary Series
Juhl’s formulae for GJMS operators and $Q$-curvatures

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Existence results for the higher-order \(Q\)-curvature equation