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

Abstract : 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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00727778
Contributor : Anne Beaulieu <>
Submitted on : Tuesday, September 4, 2012 - 1:27:01 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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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, Elsevier, 2007, 345 (7), pp.381-384. ⟨10.1016/j.crma.2007.07.010⟩. ⟨hal-00727778⟩

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