A new kind of blowing-up solutions for the Brezis-Nirenberg problem

DOI10.1007/s00526-014-0716-yzbMath1314.35050OpenAlexW2083287007MaRDI QIDQ488140

Giusi Vaira

Publication date: 23 January 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-014-0716-y

zbMATH Keywords

blowing-up solutionBrezis-Nirenberg problemsupercritical case

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20) Blow-up in context of PDEs (35B44) Positive solutions to PDEs (35B09)

Related Items

A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions ^* ⋮ Sign-changing tower of bubbles for the Brezis–Nirenberg problem ⋮ Nondegeneracy of nodal solutions to the critical Yamabe problem ⋮ Nodal Solutions of the Brezis-Nirenberg Problem in Dimension 6 ⋮ Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem

Cites Work

• Unnamed Item
• Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
• Blow-up and symmetry of sign-changing solutions to some critical elliptic equations
• 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 results of sign-changing solutions to a supercritical nonlinear problem
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• Concentration estimates and multiple solutions to elliptic problems at critical growth
• ``Bubble-tower radial solutions in the slightly supercritical Brezis-Nirenberg problem.
• Two-bubble solutions in the super-critical Bahri-Coron's problem
• Elliptic equations with critical Sobolev exponents in dimension 3
• Multi-peak solutions for super-critical elliptic problems in domains with small holes
• 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
• Some existence results for superlinear elliptic boundary value problems involving critical exponents
• On the existence and the profile of nodal solutions of elliptic equations involving critical growth
• Blow-up and nonexistence of sign changing solutions to the Brezis-Nirenberg problem in dimension three
• Sign-Changing Blow-Up for Scalar Curvature Type Equations
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Generic properties of nonlinear boundary value problems
• The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain
• MULTI-BUBBLE SOLUTIONS FOR SLIGHTLY SUPER-CRITICAL ELLIPTIC PROBLEMS IN DOMAINS WITH SYMMETRIES
• Multispike solutions for a nonlinear elliptic problem involving critical Sobolev exponent
• DOUBLE BLOW-UP SOLUTIONS FOR A BREZIS–NIRENBERG TYPE PROBLEM
• A MULTIPLICITY RESULT FOR ELLIPTIC EQUATIONS AT CRITICAL GROWTH IN LOW DIMENSION
• A NONEXISTENCE RESULT OF SINGLE PEAKED SOLUTIONS TO A SUPERCRITICAL NONLINEAR PROBLEM
• On the effect of the domain geometry on the existence of sign changing solutions to elliptic problems with critical and supercritical growth