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

Monica Musso , Frank Pacard, Juncheng Wei

• We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations ?u-u+f(u)=0 in R N , u?H 1 (R N ) , 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 D k ×O(N-2) where D k ?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) .