The Paneitz curvature problem on lower-dimensional spheres

DOI10.1007/s10455-005-9003-7zbMath1170.35394arXivmath/0305197OpenAlexW2052604502MaRDI QIDQ866981

Mohamed Ben Ayed, Khalil O. El Mehdi

Publication date: 14 February 2007

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0305197

zbMATH Keywords

critical points at infinitynoncompact variational problemsPaneitz curvature

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Elliptic equations on manifolds, general theory (58J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Higher-order elliptic equations (35J30)

Related Items (17)

Prescribing \(Q\)-curvature on higher dimensional spheres ⋮ Critical points at infinity in a fourth order elliptic problem with limiting exponent ⋮ On the positive solutions for a perturbed negative exponent problem on \(\mathbb{R}^3\) ⋮ Existence of conformal metrics with prescribed Q-curvature ⋮ Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres ⋮ Existence and concentration of positive solutions for a super-critical fourth order equation ⋮ On the prescribed Q-curvature problem on \(S^n\) ⋮ On a biharmonic equation involving slightly supercritical exponent ⋮ On a fourth order Lichnerowicz type equation involving the Paneitz-Branson operator ⋮ Conformal metrics with prescribed \(Q\)-curvature on \(S^{n}\) ⋮ Single blow-up solutions for a slightly subcritical biharmonic equation ⋮ On a fourth order elliptic equation with critical nonlinearity in dimension six ⋮ PROFILE AND EXISTENCE OF SIGN-CHANGING SOLUTIONS TO AN ELLIPTIC SUBCRITICAL EQUATION ⋮ A subcritical approximation of the Paneitz problem on spheres ⋮ Sign-changing tower of bubbles to an elliptic subcritical equation ⋮ The effect of pinching conditions in prescribing \(Q\)-curvature on standard spheres ⋮ SOME REMARKS ON THE CURVATURE TYPE PROBLEM ON

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