| Citation: |
Maoan Han. ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 788-794. doi: 10.11948/2017049
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ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD
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Abstract
In this paper, we prove smoothness of bifurcation function for a piecewise smooth periodic equation, and then use the bifurcation function together with its smoothness to study the maximum number of periodic solutions of the piecewise smooth periodic equation by the first order average.-
Keywords:
- Averaging method /
- bifurcation function /
- periodic solution /
- maximum number
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References
[1] M. Han and L. Sheng, Bifurcaton of limit cycles in piecewise smooth systems, via melnikov function, Journal of Applied Analysis and Computation, 2015, 5(4), 809-815. [2] J. Llibre and A. Mereu, Limit cycles for discontinuous quadratic differential systems, J. Math. Anal. Appl., 2014, 413, 763-775. [3] J. Llibre, A. Mereu and D. Novaes, Averaging theory for discontinuous piecewise differential systems, J. Differential Equations, 2015, 258, 4007-4032. [4] J. Llibre, D. Novaes and M. Teixeira, On the birth of limit cycles for non-smooth dynamical systems, Bull. Sci. math., 2015, 139(3), 229-244. [5] J. Llibre and M. Teixeira, Limit cycles for m-piecewise discontinuous polynomial Liénard differential equations, Z. Angew. Math. Phys., 2015, 66(1), 51-66. [6] J. Qiao and S. Shui, Limit cycles for a class of polynomial differential systems. Electron, J. Qual. Theory Differ. Equ., 2016, Paper No. 9, 9 pp. -
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Citation
Maoan Han. ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 788-794. doi: 10.11948/2017049
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