An inverse function theorem in Sobolev spaces and applications to quasi-linear Schrödinger equations

DOI10.1006/JMAA.2000.7366zbMath0988.46035OpenAlexW2007707992MaRDI QIDQ5939790

Markus Poppenberg

Publication date: 27 June 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.7366

zbMATH Keywords

Banach spacesSobolev spacesevolution equationsimplicit function theoreminverse function theorem of Nash-Moser typeloss of derivativesposednessquasi-linear Schrödinger equationquasi-linear Schrödinger equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuous and differentiable maps in nonlinear functional analysis (46T20) Derivatives of functions in infinite-dimensional spaces (46G05) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (4)

Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions ⋮ On a class of quasilinear Schrödinger equations ⋮ Sharp conditions of global existence for second‐order derivative nonlinear Schrödinger equations with combined power‐type nonlinearities ⋮ Sharp conditions of global existence for the quasilinear Schrödinger equation

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