## Weierstrass integrability of differential equations

2010
##### Authors
Giné, Jaume
Grau Montaña, Maite
##### Abstract
The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define {\it Weierstrass integrability} and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.
##### Journal or Serie
Applied Mathematics Letters, 2010, vol. 23, p. 523–526