High frequency periodic solutions of semilinear equations Solutions périodiques de haute fréquence d'équations semi-linéaires

Genevieve Allain (1) , Anne Beaulieu (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Periodic solutions bifurcation; Asymptotic behavior of solutions; Boundary value problems for higher-order elliptic equations

Domaines: Equations aux dérivées partielles [math.AP]

Genevieve Allain, Anne Beaulieu. High frequency periodic solutions of semilinear equations Solutions périodiques de haute fréquence d'équations semi-linéaires. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2007, 345 (7), pp.381-384. ⟨10.1016/j.crma.2007.07.010⟩. ⟨hal-00727778⟩