Abstract
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 limit cycles, at the same time they provide information about their stability and hyperbolicity. In this paper, we present a method to construct a special class of Dulac-Cherkas functions for generalized Lienard systems of the type dx dt = y, dy dt = ∑l j=0 hj(x)y j with l ≥ 1. In case 1 ≤ l ≤ 3, linear differential equations play a key role in this process, for l ≥ 4, we have to solve a system of linear differential and algebraic equations, where the number of equations is larger than the number of unknowns. Finally, we show that Dulac-Cherkas functions can be used to construct generalized Lienard systems with any l possessing limit cycles.
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