We build spaces of q.p. (quasi-periodic) functions and we establish some of their properties. They are motivated by the Percival approach to q.p. solutions of Hamiltonian systems. The periodic solutions of an adequat Partial Differential Equation are related to the q.p. solutions of an Ordinary Differential Equation. We use this approach to obtain some regularization theorems of weak q.p. solutions of differential equations. For a large class of differential equations, the first theorem gives a result of density: a particular form of perturbated equations have strong solutions. The second theorem gives a condition which insures that any essentially bounded weak solution is a strong one.
Publié le : 2001-07-05
Classification:
Quasi-Periodic Functions,
Ordinary Differential Equations,
42A75, 34C27, 35D10,
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA],
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00617443,
author = {Blot, Jo\"el and Pennequin, Denis},
title = {Spaces of Quasi-Periodic Functions and Oscillations in Differential Equations},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00617443}
}
Blot, Joël; Pennequin, Denis. Spaces of Quasi-Periodic Functions and Oscillations in Differential Equations. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00617443/