Journal ArticleDOI
On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
A. Bahri,Jean-Michel Coron +1 more
TLDR
Soit Ω un ensemble ouvert borne regulier et connexe de R N, N≥3. On considere u:Ω→R telle que −Δu=u (N+2)/(N−2) dans Ω, u>0 dans ǫ, u=0 sur ∂Ω as discussed by the authors.Abstract:
Soit Ω un ensemble ouvert borne regulier et connexe de R N , N≥3. On considere u:Ω→R telle que −Δu=u (N+2)/(N−2) dans Ω, u>0 dans Ω, u=0 sur ∂Ω. On note par Hd(Ω; Z 2 ) l'homologie de diemnsion d de Ω a coefficients Z 2 . S'il existe un entier positif d tel que Hd(Ω, Z 2 )¬=0, alors l'equation a une solutionread more
Citations
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Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Book
Nonlinear partial differential equations with applications
TL;DR: In this paper, the authors present a system of equations for evolving pseudomonotone or weakly continuous mappings with set-valued mappings, and a set of auxiliary tools.
Journal ArticleDOI
The role of the green's function in a non-linear elliptic equation involving the critical Sobolev exponent
TL;DR: For non-linear elliptic problems of the type (Pe), this article showed that if the ue are solutions of (Pe) which concentrate around a point as e → 0, then this point cannot be on the boundary of Ω and is a critical point of the regular part of the Green's function.
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Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent
TL;DR: In this paper, the authors study the asymptotic behavior of positive solutions of semilinear equations with nearly critical nonlinearity and show that the solutions are shown to blow up at exactly one point.
Journal Article
On positive entire solutions to a class of equations with a singular coefficient and critical exponent
TL;DR: In this paper, the authors prove existence, uniqueness and qualitative behavior of positive solutions to positive equations of the type Δ u =a(x/|x|), u+f(x,u) +n+2)/(n-2) depending on the behavior of the function $a$ of the angular variable.
References
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Journal ArticleDOI
Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
Haim Brezis,Louis Nirenberg +1 more
TL;DR: In this article, the existence of a fonction u satisfaisant l'equation elliptique non lineaire is investigated, i.e., a domaine borne in R n avec n ≥ 3.
Journal ArticleDOI
The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1
TL;DR: In this paper, the authors show how the concentration-compactness principle has to be modified in order to be able to treat this class of problems and present applications to Functional Analysis, Mathematical Physics, Differential Geometry and Harmonic Analysis.
Journal ArticleDOI
A global compactness result for elliptic boundary value problems involving limiting nonlinearities
TL;DR: On demontre l'existence de solutions nontriviales de −Δu−λu=u|u| 2 * −2 dans Ω∈R n, u/∂Ω=0 arbitrairement proches des valeurs propres λ k de − Δ:H 0 1,2 (Ω)→H − 1 (λ) as discussed by the authors
Journal ArticleDOI
Connections with l**p bounds on curvature
TL;DR: In this paper, it was shown by means of the implicit function theorem that Coulomb gauges exist for fields over a ball over compact manifolds when the integral field norm is sufficiently small.
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Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
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