On the existence of blowing-up solutions for a mean field equation ? ? The first and second authors

By P. Esposito, M. Grossi, Angela Pistoia. 2005

226 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e6da1dd6f2295e39b06de72b68bc051b1c139db1

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

In Numerical Analysis

Citations in the corpus

Multiple Blow-Up Phenomena for the Sinh-Poisson Equation (2012, background): “[15] built positive solutions whose concentration points, as λ goes to zero, are critical points for the”
Nonexistence of multi-bubble solutions to some elliptic equations on convex domains (2010, background): “Our results are in striking contrast with the existence of blowing-up solutions at multiple blow-up points on domains which meet some topological or geometrical conditions, see [2,10, 9].”
Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity (2006, unknown): “This problem is very much in the spirit of the work of [8] and [5] even though we do no know any applications in physics.”
New solutions for Trudinger–Moser critical equations in R2 (2010, background): “It is interesting to mention the link of the above discovered concentration phenomena with the related Liouville equation u+ λe = 0 under Dirichlet boundary condition in a bounded domain Ω in R2, see [8,13,15] and references therein.”
Nondegeneracy of entire solutions of a singular Liouvillle equation (2012, methodology): “This property has been used for instance in [1, 6, 9] to build solutions with multiple concentration points for the problem Δu+ ε(2)e = 0 in Ω, u = 0 on ∂Ω, as ε → 0 where Ω is a bounded domain in R(2).”
Bubbling solutions for an anisotropic Emden–Fowler equation (2006, background): “Conversely, many authors have tried to construct blow-up solutions, see [2,5,7].”
ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN (2013, background): “The rest part of the proof goes along the same way to [24] or [13], where the authors considered domains Ωǫ consisting of k disjoint balls and thin strips liking them whose widths are ǫ.”