Resultados de existência e de não existência de ciclos limites e nós em equações diferenciais ordinárias

Abstract

Nodes are equilibria of a planar differential equation or vector field whose eigenvalues have the same sign. Star nodes are nodes whose eigenvalues are equal and nonzero. Limit cycles are closed and isolated orbits in the set of closed orbits of a vector field. This work aims to find conditions, as general as possible, in order to guarantee the coexistence of limit cycles and star nodes. Such a study is done in a convenient way: take a family of differential equations whose origin is a star node equilibrium and searches for conditions for the existence of a limit cycle around the origin. Later, the study is generalized and some results contemplate other types of equilibria.