Two-bubble solutions in the super-critical Bahri-Coron's problem

By Manuel del Pino, Patricio Felmer, Monica Musso. 2003

187 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/005e81f1295a4e4e68e74b397cc63b55e9cc5216

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Super-critical boundary bubbling in a semilinear Neumann problem (2005, methodology): “The proofs of Theorems 1 and 2 rely on a form of Lyapunov–Schmidt procedure which reduces the construction of the searched solutions to a finite-dimensional variational problem, in a general scheme already followed in the study of interior bubbling in [ 10 ,8].”
On the Existence and the Profile of Nodal solutions of Elliptic Equations Involving Critical Growth (2006, background): “Related methods can be found in [5,7,17,27,30,31].”
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005, methodology): “Such a method has been used successfully in many papers, see e.g. [1], [2], [ 7 ], [11], [12], [13].”
Tower of bubbles for almost critical problems in general domains (2010, background): “The proof of the results contained in [5], [6], [8], [16] is based on a version of the Liapunov-Schmidt reduction (see [9]) in the class of radially symmetric functions with bounded weighted L1-norm (see also [ 7 ]).”
Singular limits in Liouville-type equations (2005, methodology): “been used in [ 17 , 18] to detect bubbling from above the critical exponent in higher dimensional problems improving the method in [1, 29], both in lifting criticality (or subcriticality) required there, and non-degeneracy of critical points of the analogue of ’m in that context.”
Bubbling solutions for an anisotropic Emden–Fowler equation (2006, unknown): “other papers. See for instance [4], [ 11 ], [9], [15], [16], [17], [13], [25] and references therein.”
The Supercritical Lane–Emden–Fowler Equation in Exterior Domains (2007, background): “If p is super-critical but close to critical, solvability still holds in domains with small holes (see del Pino et al, 2003 ).”
THE BREZIS-NIRENBERG PROBLEM NEAR CRITICALITY IN DIMENSION 3 ? (2004, unknown): “Bubbling from above the critical exponent when = 0 in domains exhibiting small holes was found in [ 10 ].”