Quasi-periodic solutions with Sobolev regularity of NLS on with a multiplicative potential
Massimiliano Berti, Philippe Bolle (2013)
Journal of the European Mathematical Society
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We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on , finitely differentiable 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 then the solutions are . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized...