Abstract In this paper, we consider a Van der Pol oscillator with state-dependent delay. Firstly, we seek for a suitable set E on which we construct a Poincar\'e operator F. Then, we prove that the operator F is continuous and compact on E\0\. After that, we obtain the ejectivity of the trivial fixed point \0\ and the existence of slowly oscillating periodic solution. Finally, we choose an example of state-dependent delay to test our analytical result by comparing it to numerical continuation.This theoretical result generalizes and improves some existing results.
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Hou et al. (2024) studied this question.
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