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Published on: February 3, 2014
Bifurcations of degenerate homoclinic solutions in discontinuous systems under non-autonomous perturbations
1School of Mathematical Sciences, Key Laboratory of MEA (Ministry of Education), Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, People's Republic of China.
Abstract:
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.
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