Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries

DOI10.1016/j.anihpc.2013.01.001zbMath1288.35212arXiv1208.5892OpenAlexW1968467668MaRDI QIDQ2446367

Teresa D'Aprile, Thomas J. Bartsch, Angela Pistoia

Publication date: 16 April 2014

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5892

zbMATH Keywords

finite-dimensional reductionsign-changing solutionsmax-min argumentslightly subcritical problem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear boundary value problems for linear elliptic equations (35J65) Variational methods for second-order elliptic equations (35J20)

Related Items

Stabilization of arbitrary structures in a doubly degenerate reaction-diffusion system modeling bacterial motion on a nutrient-poor agar ⋮ Entire nodal solutions to the pure critical exponent problem arising from concentration ⋮ Concentration with a single sign-changing layer at the higher critical exponents ⋮ New type of solutions to a slightly subcritical Hénon type problem on general domains ⋮ Nonlinear Schrödinger equations near an infinite well potential ⋮ Nodal bubble tower solutions to slightly subcritical elliptic problems with Hardy terms ⋮ Efficient gluing of numerical continuation and a multiple solution method for elliptic PDEs ⋮ Nodal blow-up solutions to slightly subcritical elliptic problems with Hardy-critical term ⋮ Multi-bubble nodal solutions to slightly subcritical elliptic problems with Hardy terms in symmetric domains ⋮ A new type of nodal solutions to singularly perturbed elliptic equations with supercritical growth

Cites Work

• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Proof of two conjectures of H. Brezis and L. A. Peletier
• Multiplicity of solutions to the supercritical Bahri--Coron's problem in pierced domains
• Nonexistence of multi-bubble solutions to some elliptic equations on convex domains
• Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
• Blow-up points of solutions to elliptic equations with limiting nonlinearity
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots
• Two-bubble solutions in the super-critical Bahri-Coron's problem
• On the strict concavity of the harmonic radius in dimension \(N\geq 3\)
• Multi-peak solutions for super-critical elliptic problems in domains with small holes
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• A note on additional properties of sign changing solutions to superlinear elliptic equations
• Classification of low energy sign-changing solutions of an almost critical problem
• 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
• On the profile of sign-changing solutions of an almost critical problem in the ball
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Remarks on some quasilinear elliptic equations
• MULTI-BUBBLE SOLUTIONS FOR SLIGHTLY SUPER-CRITICAL ELLIPTIC PROBLEMS IN DOMAINS WITH SYMMETRIES
• Critical point theory on partially ordered Hilbert spaces
• Unnamed Item
• Unnamed Item