High frequency periodic solutions of semilinear equations Solutions périodiques de haute fréquence d'équations semi-linéaires
Résumé
We are interested with positive solutions of −ε2Δu+f(u)=0 in S1×R, i.e. periodic solutions in the first coordinate x1. The model function for f is f(u)=u−up, p>1. We prove that for ε large enough, any positive solution is a function of the second coordinate only.