A surjection theorem for maps with singular perturbation and loss of derivatives

DOI10.4171/JEMS/1086MaRDI QIDQ2039605

Ivar Ekeland, Éric Séré

Publication date: 5 July 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.07568

zbMATH Keywords

Cauchy problemsingular perturbationsEkeland's variational principleloss of derivativesnonlinear Schrödinger systemNash-Moser theoreminverse function theorem

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Singular perturbations in context of PDEs (35B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for nonlinear higher-order PDEs (35G25) Implicit function theorems; global Newton methods on manifolds (58C15) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)

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Cites Work

• An inverse function theorem in Fréchet spaces
• Nash-Moser iteration and singular perturbations
• The imbedding problem for Riemannian manifolds
• An abstract Nash-Moser theorem with parameters and applications to PDEs
• Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions
• Inversion of smooth mappings
• Cantor families of periodic solutions for completely resonant wave equations
• The boundary problems of physical geodesy
• A Nash-Moser-Hörmander implicit function theorem with applications to control and Cauchy problems for PDEs
• Cantor families of periodic solutions for completely resonant nonlinear wave equations
• A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
• Dispersive stabilization
• The inverse function theorem of Nash and Moser
• On quasi‐isometric mappings, I
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