Abstract. The purpose of this paper is to give sufficient conditions under which an equivalent system to the equation (φp(ẋ))˙+ f(x)φp(ẋ) + g(x) = 0 has at least one stable limit cycle, where φp(·) is the one-dimensional p-Laplacian. The main results are proved by means of phase plane analysis with the Poincaré-Bendixson theorem. Sufficient conditions are also given for the origin (x,ẋ) = (0, 0) to be unstable and for all solutions to be bounded in the future.2000 Mathematics Subject Classification: 34C05, 34C07, 70K05, 70K42.

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