Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Gabriel Thomas
Pages: [145] - [155]
Received Date: April 25, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121661
Let an ODE 
where F is analytic in 
The singular locus is the set 
We are interested in the algebraic
conditions for singular solutions to happen.
First we deal with the analytic case: the graph of a singular solution
is embedded in S. We recall that such a solution may occur only
when the differential ideal generated by 
is not reducible. The existence of
singular solutions is not generic and we show a relationship with the
theory of differential-algebraic equations by Rabier and Rheinboldt
[9]. This is also the adaptation to holomorphic differential equations
of a result from Fukuda and Fukuda [2].
On the other hand, the Ritt-Raudenbusch theorems, related to the
decomposition of differential ideals, give the algebraic conditions to
get singular solutions for polynomial differential systems. This also
indicates the non genericity of singular solutions existence.
non-linear differential equations, singular solution, decomposition theorem.
