## 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

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