[1] Di Bernardo M, Budd C J, Champneys A R, et al.Piecewise-Smooth Dynamical Systems: Theory and Applications. London: Springer-Verlag, 2008
[2] Shahshahani S. Periodic solutions of polynomial first order differential equations. Nonlinear Analysis: Theory Methods & Applications, 1981, 5(2): 157-165
[3] Neto A L. On the number of solutions of the equation $\frac{{\rm d}x}{{\rm d}t} = \sum\limits_{j = 0}^n a_j (t) x^j, 0 \leq t \leq 1, $ for which $x (0)= x (1)$. Inventiones Mathematicae, 1980, 59(1): 67-76
[4] Lloyd N G. The number of periodic solutions of the equation $\frac{{\rm d}z}{{\rm d}t}=z^N+p_1(t)z^{N-1}+\cdots+p_{N}(t)$. Proceedings of the London Mathematical Society, 1973, 27(3): 667-700
[5] Sheng L, Han M.Periodic solutions of one dimensional periodic differential equations
(in Chinese). Sci Sin Math, 2017, 47(1): 171-186
[6] Buica A, Llibre J. Averaging methods for finding periodic orbits via Brouwer degree. Bulletin Des Sciences Mathematiques, 2004, 128(1): 7-22
[7] Buica A, Francoise J P, Llibre J. Periodic solutions of nonlinear periodic differential systems with a small parameter. Communications on Pure and Applied Analysis, 2007, 6(1): 103-111
[8] Llibre J, Novaes D, Rodrigues C. Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones. Physica D: Nonlinear Phenomena, 2017, 353/354: 1-10
[9] Sheng L, Wang S, Li X, et al. Bifurcation of periodic orbits of periodic equations with multiple parameters by averaging method. Journal of Nonlinear Modeling and Analysis, 2020, 490(2): 124311
[10] Han M, Yang J. The maximum nonumber of zero of functions with parameters and application to differential equations. Journal of Nonlinear Modeling and Analysis, 2021, 3(1): 13-34
[11] Han M. On the maximum number of periodic solutions of piecewise smooth periodic equations by average method. Journal of Applied Analysis & Computation, 2017, 7(2): 788-794
[12] Lloyd N G. A note on the number of limit cycles in certain two-dimensional systems. Journal of the London Mathematical Society, 1979, 20(2): 277-286
[13] Hou W, Liu S. Melnikov functions for a class of piecewise Hamiltonian systems. Journal of Nonlinear Modeling and Analysis, 2023, 5(1): 123-145 |