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The main aim of this paper is to study bifurcations of bounded solutions from a degenerate homoclinic solution for discontinuous systems under non-autonomous perturbations. We use Lyapunov–Schmidt reduction to give bifurcation equations and prove that a single parameter is enough to unfold two distinct homoclinic solutions bifurcated from the unperturbed degenerate homoclinic solution. Furthermore, we give an example of a periodically perturbed piecewise smooth differential equation in R4 to support our conclusions.
Hua et al. (Sat,) studied this question.