Skip to Main content Skip to Navigation

Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation.

Abstract : We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations Δu−u+f(u)=0 in RN, u∈H1(RN), where N≥2. Under natural conditions on the nonlinearity f, we prove the existence of infinitely many nonradial solutions in any dimension N≥2. Our result complements earlier works of Bartsch and Willem (N=4 or N≥6) and Lorca-Ubilla (N=5) where solutions invariant under the action of O(2)×O(N−2) are constructed. In contrast, the solutions we construct are invariant under the action of Dk×O(N−2) where Dk⊂O(2) denotes the dihedral group of rotations and reflexions leaving a regular planar polygon with k sides invariant, for some integer k≥7, but they are not invariant under the action of O(2)×O(N−2).
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00851584
Contributor : Carole Juppin <>
Submitted on : Thursday, August 15, 2013 - 12:08:42 AM
Last modification on : Thursday, March 5, 2020 - 6:26:00 PM

Identifiers

  • HAL Id : hal-00851584, version 1

Collections

Citation

Frank Pacard, Monica Musso, Juncheng Wei. Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation.. J. Eur. Math. Soc., 2012, 14 (6), pp.923-1953. ⟨hal-00851584⟩

Share

Metrics

Record views

160