Tower of bubbles for almost critical problems in general domains

DOI10.1016/j.matpur.2009.08.001zbMath1183.35143OpenAlexW2004167700MaRDI QIDQ2655043

Angela Pistoia, Monica Musso

Publication date: 22 January 2010

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/141387

zbMATH Keywords

critical Sobolev exponentblowing-up solutionRobin's functiontower of bubbles

Mathematics Subject Classification ID

Attractors (35B41) Fundamental solutions to PDEs (35A08) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (36)

Boundary bubbling solutions for a supercritical Neumann problem with mixed nonlinearities ⋮ Nodal bubble-tower solutions for a semilinear elliptic problem with competing powers ⋮ A solution to a slightly subcritical elliptic problem with non-power nonlinearity ⋮ Entire nodal solutions to the pure critical exponent problem arising from concentration ⋮ Sign-changing bubble tower solutions for a critical fractional problem ⋮ Concentration with a single sign-changing layer at the higher critical exponents ⋮ Bubble-tower solutions to asymptotically critical nonlocal elliptic equations on conformal infinities ⋮ New type of solutions to a slightly subcritical Hénon type problem on general domains ⋮ Boundary-layers for a Neumann problem at higher critical exponents ⋮ Boundary clustered layers near the higher critical exponents ⋮ Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds ⋮ Multispike solutions for a slightly subcritical elliptic problem with non-power nonlinearity ⋮ On a biharmonic elliptic problem with slightly subcritical non-power nonlinearity ⋮ Nonlinear Schrödinger equations near an infinite well potential ⋮ Positive solutions of the Gross–Pitaevskii equation for energy critical and supercritical nonlinearities ⋮ Existence of Solutions to a Slightly Supercritical Pure Neumann Problem ⋮ Sign-changing bubble tower solutions for a supercritical elliptic problem with the Hénon term ⋮ Spiked solutions for fractional Schrödinger systems with Sobolev critical Exponent ⋮ Boundary towers of layers for some supercritical problems ⋮ Multiple blow-up phenomena for the sinh-Poisson equation ⋮ Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries ⋮ Nodal bubble tower solutions to slightly subcritical elliptic problems with Hardy terms ⋮ Supercritical problems in domains with thin toroidal holes ⋮ Multiplicity of solutions to nearly critical elliptic equation in the bounded domain of \(\mathbb{R}^3\) ⋮ Existence and nonexistence of sign-changing solutions to elliptic critical equations ⋮ Sign-changing solutions for critical equations with Hardy potential ⋮ Nodal blow-up solutions to slightly subcritical elliptic problems with Hardy-critical term ⋮ Towering phenomena for the Yamabe equation on symmetric manifolds ⋮ Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains ⋮ A subcritical approximation of the Paneitz problem on spheres ⋮ Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian ⋮ New type of solutions to a slightly subcritical Hénon type problem in dimensions 7, 8 and 9 ⋮ Multi-bubble nodal solutions to slightly subcritical elliptic problems with Hardy terms in symmetric domains ⋮ Sign-changing tower of bubbles to an elliptic subcritical equation ⋮ Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions \(n \geq 7\) ⋮ Blow up of solutions of semilinear heat equations in general domains

Cites Work

• On the nondegeneracy of the critical points of the Robin function in symmetric domains
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
• 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.
• Concentration phenomena in elliptic problems with critical and supercritical growth.
• Two-bubble solutions in the super-critical Bahri-Coron's problem
• 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
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Existence of blowing-up solutions for a slightly subcritical or a slightly supercritical nonlinear elliptic equation on \(\mathbb R^n\)
• Constant scalar curvature metrics with isolated singularities
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
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