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arxiv: 1401.0271 · v1 · pith:NZGFXBPFnew · submitted 2014-01-01 · 🧮 math.AP

Solutions without any symmetry for semilinear elliptic problems

classification 🧮 math.AP
keywords symmetrydeltaellipticenergyequationexistencefinitegroup
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We prove the existence of infinitely many solitary waves for the nonlinear Klein-Gordon or Schr\"odinger equation $$ \Delta u-u+ u^3 =0 , $$ in ${\bf R}^2$, which have finite energy and whose maximal group of symmetry reduces to the identity.

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