Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains

DOI10.1080/03605302.2010.490286zbMath1205.35096OpenAlexW2056491280MaRDI QIDQ4933523

Angela Pistoia, Yuxin Ge, Monica Musso

Publication date: 14 October 2010

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2010.490286

zbMATH Keywords

critical Sobolev exponentblowing-up solutionRobin's functiontower of bubbles

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Blow-up in context of PDEs (35B44) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (26)

Boundary bubbling solutions for a supercritical Neumann problem with mixed nonlinearities ⋮ Entire nodal solutions to the pure critical exponent problem arising from concentration ⋮ Sign-changing bubble tower solutions for a critical fractional problem ⋮ Infinitely many non-radial solutions to a critical equation on annulus ⋮ Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents ⋮ Boundary clustered layers near the higher critical exponents ⋮ Sign-changing bubble towers for asymptotically critical elliptic equations on Riemannian manifolds ⋮ Concentration on the Clifford torus for the critical problem in an annulus ⋮ A critical elliptic problem involving fractional Laplacian operator in domains with shrinking holes ⋮ Multiple solutions to a weakly coupled purely critical elliptic system in bounded domains ⋮ Sign-changing bubble tower solutions for a supercritical elliptic problem with the Hénon term ⋮ Coron's problem for the critical Lane-Emden system ⋮ Boundary towers of layers for some supercritical problems ⋮ Multiple blow-up phenomena for the sinh-Poisson equation ⋮ High energy sign-changing solutions for Coron's problem ⋮ Supercritical problems in domains with thin toroidal holes ⋮ Existence and nonexistence of sign-changing solutions to elliptic critical equations ⋮ Existence and asymptotic profile of nodal solutions to supercritical problems ⋮ On the influence of second order uniformly elliptic operators in nonlinear problems ⋮ Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian ⋮ A fountain of positive bubbles on a Coron's problem for a competitive weakly coupled gradient system ⋮ Nondegeneracy of the bubble for the critical p-Laplace equation ⋮ Sign-changing tower of bubbles to an elliptic subcritical equation ⋮ Multiple solutions to the Bahri-Coron problem in some domains with nontrivial topology ⋮ Multiple solutions to the Bahri–Coron problem in domains with a shrinking hole of positive dimension ⋮ Positive solutions to a supercritical elliptic problem that concentrate along a thin spherical hole

Cites Work

• Unnamed Item
• Sign changing solutions to a nonlinear elliptic problem involving the critical Sobolev exponent in pierced domains
• Sign changing solutions to a Bahri-Coron's problem in pierced domains
• Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
• Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole
• A note on the Sobolev inequality
• Best constant in Sobolev inequality
• Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• ``Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem.
• An elliptic problem with critical growth in domains with shrinking holes.
• Linear forms in multiple zeta values and multiple integrals
• 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
• Existence of blowing-up solutions for a slightly subcritical or a slightly supercritical nonlinear elliptic equation on \(\mathbb R^n\)
• A note on additional properties of sign changing solutions to superlinear elliptic equations
• Minimal nodal solutions of the pure critical exponent problem on a symmetric domain
• Prescribing scalar curvature on \(\mathbb{S}^ n\) and related problems. I
• Constant scalar curvature metrics with isolated singularities
• On the existence and the profile of nodal solutions of elliptic equations involving critical growth
• Tower of bubbles for almost critical problems in general domains
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• TWO SOLUTIONS OF THE BAHRI–CORON PROBLEM IN PUNCTURED DOMAINS VIA THE FIXED POINT TRANSFER
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Remarks on some quasilinear elliptic equations
• The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain
• On the effect of the domain geometry on the existence of sign changing solutions to elliptic problems with critical and supercritical growth

This page was built for publication: Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains