Abstract:
In this paper we give an explicit expression of invariant algebraic curves
of multi-parameter planar polynomial differential systems of degree nine, then we
prove that these systems are integrable and we introduce an explicit expression of
a first integral. Moreover, we determine sufficient conditions for these systems to
possess two limit cycles: one of them is algebraic and the other one is shown to be
non-algebraic, explicitly given. Concrete examples exhibiting the applicability of our
result are introduced.
Keywords and phrases:limit cycle, Riccati equation, invariant algebraic curve, first integral.