The analytic domain in the implicit function theorem.
The Nash-Moser inverse mapping theorem
The rate of convergence of a modified Newton's process
Théorie du degré dans certains espaces de Fréchet d'après R. S. Hamilton
Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.