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In this paper, we study the limit cycles of a kind of Li e nar d systemwith a nilpotent center under perturbations. Let L(m; n) denote the numberof limit cycles of this Li e nard system ẋ = y- ɛ F(x) ; ẏ =-g (x) near theorigin, where m = deg g; n = deg F. We o btain some results of L(m; n) for m = 4; 2 n ≤ 20, m = 5, 2 ≤ 10, m = 6, 2 ≤ n ≤ 5, m = 7, 2 ≤ n ≤ 4, where some results are new.

ON THE LIMIT CYCLES OF A KIND OF LI&#201;NARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS

ON THE LIMIT CYCLES OF A KIND OF LIÉNARD SYSTEM WITH A NILPOTENT CENTER UNDER PERTURBATIONS