Existence of global solutions for a class of vector fields on the three-dimensional torus
Publication date: October 2018
Source: Bulletin des Sciences Mathématiques, Volume 148
Author(s): Adalberto P. Bergamasco, Paulo L. Dattori da Silva, Rafael B. Gonzalez
This work deals with global solvability of a class of vector fields of the form , where and , defined on the three-dimensional torus . In addition to the interplay between the order of vanishing of the functions a and b, the change of sign of b between two consecutive zeros of has influence in the global solvability. Also, a Diophantine condition appears in a natural way in our results.