Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds

DOI10.1016/j.jde.2013.02.017zbMath1288.58013OpenAlexW2151539693MaRDI QIDQ393031

Angela Pistoia, Jérôme Vétois

Publication date: 15 January 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2013.02.017

zbMATH Keywords

Riemannian manifoldLaplace-Beltrami operatorasymptotically critical equationselliptic equations on manifoldsYamabe potential

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Elliptic equations on manifolds, general theory (58J05)

Related Items (14)

Blow-up solutions for Hardy-Sobolev equations on compact Riemannian manifolds ⋮ Bubble-tower solutions to asymptotically critical nonlocal elliptic equations on conformal infinities ⋮ Clustered solutions for supercritical elliptic equations on Riemannian manifolds ⋮ The Lin-Ni conjecture in negative geometries ⋮ Stationary Kirchhoff equations with powers ⋮ Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part ⋮ Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold ⋮ Compactness and non-compactness for Yamabe-type problems ⋮ Bubbling above the threshold of the scalar curvature in dimensions four and five ⋮ Recent results on stationary critical Kirchhoff systems in closed manifolds ⋮ Stability and instability results for sign-changing solutions to second-order critical elliptic equations ⋮ New Type of Sign-Changing Blow-up Solutions for Scalar Curvature Type Equations ⋮ Sign-changing blow-up for the Yamabe equation at the lowest energy level ⋮ Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Infinitely many solutions for the Schrödinger equations in \(\mathbb R^N\) with critical growth
• Large energy entire solutions for the Yamabe equation
• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Nodal bubble-tower solutions to radial elliptic problems near criticality
• Compactness of solutions to the Yamabe problem. III
• A compactness theorem for the Yamabe problem
• Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
• Blow-up phenomena for the Yamabe equation. II
• Bounded stability for strongly coupled critical elliptic systems below the geometric threshold of the conformal Laplacian
• On a conformally invariant elliptic equation on \(R^ n\)
• A note on the Sobolev inequality
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• ``Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem.
• Large energy entire solutions for the Yamabe type problem of polyharmonic operator
• Super-critical boundary bubbling in a semilinear Neumann problem
• The Brezis-Nirenberg problem near criticality in dimension 3
• Bubble towers for supercritical semilinear elliptic equations
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• A Harnack type inequality for the Yamabe equation in low dimensions
• Bubble tower solutions of slightly supercritical elliptic equations and application in symmetric domains
• A priori estimates for the Yamabe problem in the non-locally conformally flat case
• The conjectures on conformal transformations of Riemannian manifolds
• Compactness of solutions to the Yamabe problem. II
• Tower of bubbles for almost critical problems in general domains
• Blow-up phenomena for the Yamabe equation
• Blow-up solutions for asymptotically critical elliptic equations on Riemannian manifolds
• YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS
• Torus action on S^n and sign changing solutions for conformally invariant equations
• Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains
• MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS ON COMPACT RIEMANNIAN MANIFOLDS

This page was built for publication: Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds