New result of existence of periodic solutions for a generalized p-Laplacian Liénard type differential equation with a variable delay

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In this paper, we propose a generalized [Formula: see text]-Laplacian Liénard type differential equation with a variable delay. By applying the Mawhin continuation theorem, we established a set of sufficient conditions on the existence of at least one periodic solution with period [Formula: see text]. It is significant that the growth degree with respect to the variables [Formula: see text] imposed on [Formula: see text] is allowed to be greater than [Formula: see text] and the growth degree with respect to the variables [Formula: see text] imposed on [Formula: see text] is allowed to be greater than [Formula: see text] so the result not only improves but also generalizes. Some examples are provided to illustrate the results.