We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations in , , where . Under natural conditions on the nonlinearity , we prove the existence of infinitely many nonradial solutions in any dimension . Our result complements earlier works of Bartsch and Willem ( or ) and Lorca-Ubilla () where solutions invariant under the action of are constructed. In contrast, the solutions we construct are invariant under the action of where denotes the dihedral group of rotations and reflexions leaving a regular planar polygon with sides invariant, for some integer , but they are not invariant under the action of .
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Juncheng Wei, Monica Musso, Frank Pacard, Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation. J. Eur. Math. Soc. 14 (2012), no. 6, pp. 1923–1953DOI 10.4171/JEMS/351