Partial Di ¤ erential Equations — Quasi - periodic solutions of Nonlinear

نویسندگان

  • Massimiliano Berti
  • Giovanni Prodi
چکیده

— We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T , db 1, finitely di¤erentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are in Cl then the solutions are in Cl. The proofs are based on an improved Nash–Moser iterative scheme and a new multiscale inductive analysis for the inverse linearized operators.

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تاریخ انتشار 2011