Sur une équation elliptique non linéaire avec l’exposant critique de Sobolev. (On a nonlinear elliptic equation involving the critical Sobolev exponent). (French) Zbl 0601.35040

Bahri, Abbas; Coron, Jean-Michel

C. R. Acad. Sci., Paris, Sér. I 301, 345-348 (1985).

We prove the existence of a positive solution u of the equation \(\Delta u+u^ 5=0\), \(u=0\) on \(\partial \Omega\) where \(\Omega\) is a non contractible open bounded set in \({\mathbb{R}}^ 3\).

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35B05	Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

critical Sobolev exponent; existence; positive solution