We consider two-dimensional smooth vector fields $ dx/dt= P (x, y), dy/dt= Q (x, y) $ and
estimate the maximal number of limit cycles with special properties which are defined by …

Dulac-Cherkas functions can be used to derive an upper bound for the number of limit
cycles of planar autonomous differential systems including criteria for the non-existence of …

In the class of planar autonomous quadratic polynomial differential systems we provide 6
different phase portraits having exactly 3 limit cycles surrounding a focus, 5 of them have a …

Consider the class of systems dxdt= y, dydt=− x+ μ∑ j= 0 3 hj (x, μ) yj depending on the real
parameter μ. We are concerned with the inverse problem: How to construct the functions hj …

The earlier-developed approach to the solution of the problem of estimating the number of
limit cycles and their localization for autonomous systems on the plane with the use of Dulac …

To estimate the number and location of limit cycles of Kukles systems in a strip of the phase
plane xOy, we develop a method for constructing the Dulac function in the form of a …

Our key assumptions with resp ect to the extended system (1. 2) are the following ones.(A2).
There isa smooth functional m: dom m C Ω→ I such that system (1. 2) has an invariant …

For autonomous systems on the real plane, we develop a regular method for localizing and
estimating the number of limit cycles surrounding the unique singular point. The method is to …

Discusses a precise estimate of the number of limit cycles of autonomous systems on the
plane. Method for estimating the number of limit cycles of the system with the use of a …

The article presents calculations on an estimate of the number of Limit Cycles via critical
points of Conditional Extremum. The minimum is taken with respect to the phase variables …