We present a Frobenius type theorem for a system of nonlinear partial differential equations. Typical application is the normal form theory of a singular vector field. The construction of a singular solution is closely related with a Riemann-Hilbert factorization.
Publié le : 2008-01-15
Classification:
Fuchsian equation,
Frobenius method,
Riemann-Hilbert problem,
normal form,
resonance,
34M35,
35L40,
35Q15
@article{1206367962,
author = {YOSHINO, Masafumi and SHIRAI, Akira},
title = {Singular solutions of nonlinear partial differential equations with resonances},
journal = {J. Math. Soc. Japan},
volume = {60},
number = {1},
year = {2008},
pages = { 237-263},
language = {en},
url = {http://dml.mathdoc.fr/item/1206367962}
}
YOSHINO, Masafumi; SHIRAI, Akira. Singular solutions of nonlinear partial differential equations with resonances. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp. 237-263. http://gdmltest.u-ga.fr/item/1206367962/