|
[1]
|
C. Bereanu and J. Mawhin, Periodic solutions of nonlinear perturbations of Φ-Laplacians with possibly bounded Φ, Nonlinear Anal., 68 (2008), 1668–1681. doi: 10.1016/j.na.2006.12.049.
|
|
[2]
|
H. Brezis and J. Mawhin, Periodic solutions of the forced relativistic pendulum, Differential Integral Equations, 23 (2010), 801–810.
|
|
[3]
|
C. Bereanu and P.J. Torres, Existence of at least two periodic solutions of the forced relativistic pendulum, Proc. Amer. Math. Soc., 140 (2012), 2713–2719. doi: 10.1090/S0002-9939-2011-11101-8.
|
|
[4]
|
C. Bereanu, P. Jebelean and J. Mawhin, Periodic solutions of pendulum-like perturbations of singular and bounded Φ-Laplacians, J. Dynam. Differential Equations, 22 (2010), 463–471. doi: 10.1007/s10884-010-9172-3.
|
|
[5]
|
C. Bereanu and J. Mawhin, Existence and multiplicity results for some nonlinear problems with singular Φ-Laplacian, J. Differential Equations, 243 (2007), 536–557. doi: 10.1016/j.jde.2007.05.014.
|
|
[6]
|
J. Chu and M. Li, Twist periodic solutions of second order singular differential equations, J. Math. Anal. Appl., 355 (2009), 830–838. doi: 10.1016/j.jmaa.2009.02.033.
|
|
[7]
|
J. Chu, P. J. Torres and F. Wang, Radial stability of periodic solutions of the GyldenMeshcherskii-type problem, Discrete Contin. Dyn. Syst., 35 (2015), 1921–1932. doi: 10.3934/dcds.2015.35.1921.
|
|
[8]
|
J. Chu, P.J. Torres and F. Wang, Twist periodic solutions for differential equations with a combined attractive-repulsive singularity, J. Math. Anal. Appl., 437 (2016), 1070–1083. doi: 10.1016/j.jmaa.2016.01.057.
|
|
[9]
|
J. Chu, N. Fan and P. J. Torres, Periodic solutions for second order singular damped differential equations, J. Math. Anal. Appl., 388 (2012), 665–675. doi: 10.1016/j.jmaa.2011.09.061.
|
|
[10]
|
J. Chu, P.J. Torres and M. Zhang, Periodic solutions of second order non-autonomous singular dynamical systems, J. Differential Equations, 239 (2007), 196–212. doi: 10.1016/j.jde.2007.05.007.
|
|
[11]
|
J.Á. Cid and P.J. Torres, On the existence and stability of periodic solutions for pendulum-like equations with friction and Φ-Laplacian, Discrete Contin. Dyn. Syst., 33 (2013), 141–152. doi: 10.3934/dcds.2013.33.141.
|
|
[12]
|
F. Forbat and A. Huaux, Détermination approchée et stabilité locale de la solution périodique d'une équation différentielle non linéaire, Mém. Publ. Soc. Sci. Arts Lett. Hainaut., 76 (1962), 3–13.
|
|
[13]
|
A. Fonda and R. Toader, Periodic orbits of radially symmetric Keplerian-like systems: A topological degree approach, J. Differential Equations, 244 (2008), 3235–3264. doi: 10.1016/j.jde.2007.11.005.
|
|
[14]
|
D. Franco and P. J. Torres, Periodic solutions of singular systems without the strong force condition, Proc. Amer. Math. Soc., 136 (2008), 1229–1236. doi: 10.1090/S0002-9939-07-09226-X.
|
|
[15]
|
R. Hakl and P. J. Torres, On periodic solutions of second-order differential equations with attractive-repulsive singularities, J. Differential Equations, 248 (2010), 111–126. doi: 10.1016/j.jde.2009.07.008.
|
|
[16]
|
A. Huaux, Sur L'existence d'une solution périodique de l'e quation différentielle non linéaire $\ddot x + (0, 2)\dot x + \frac{x}{{1 -x}} = (0, 5)$ cos ωt, Bull. Cl. Sci. Acad. R. Belguique, 48 (1962), 494–504.
|
|
[17]
|
J. Mawhin, Periodic solutions of the forced pendulum: classical vs relativistic, Matematiche, 65 (2010), 97–107.
|
|
[18]
|
R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equation, Lecture notes in Mathematics, vol. 568 Berlin: Springer-Verlag, 1977.
|
|
[19]
|
R. Ortega, Stability of a periodic problem of Ambrosetti-Prodi type, Differential Integral Equations, 3 (1990), 275–284.
|
|
[20]
|
R. Ortega, Stability and index of periodic solutions of an equation of Duffing type, Boll. Un. Mat. Ital. B, 3 (1989), 533–546.
|
|
[21]
|
R. Ortega, Some applications of the topological degree to stability theory, in Topological methods in differential equations and inclusions (Montreal, PQ, 1994), 377–409, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , 472, Kluwer Acad. Publ. , Dordrecht, 1995.
|
|
[22]
|
R. Ortega, Stability and index of periodic solutions of a nonlinear telegraph equation, Commun. Pure Appl. Anal., 4 (2005), 823–837. doi: 10.3934/cpaa.2005.4.823.
|
|
[23]
|
H. N. Pishkenari, M. Behzad and A. Meghdari, Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation, Chaos Solitons Fractals, 37 (2008), 748–762.
|
|
[24]
|
S. Rützel, S. I. Lee and A. Raman, Nonlinear dynamics of atomic-force-microscope probes driven in Lennard-Jones potentials, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci., 459 (2003), 1925–1948.
|
|
[25]
|
P. J. Torres, Twist solutions of a Hill's equations with singular term, Adv. Nonlinear Stud., 2 (2002), 279–287. doi: 10.1515/ans-2002-0305.
|
|
[26]
|
P. J. Torres and M. Zhang, Twist periodic solutions of repulsive singular equations, Nonlinear Anal., 56 (2004), 591–599. doi: 10.1016/j.na.2003.10.005.
|
|
[27]
|
P. J. Torres, Existence and stability of periodic solutions for second-order semilinear differential equations with a singular nonlinearity, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 195–201. doi: 10.1017/S0308210505000739.
|
|
[28]
|
P. J. Torres, Periodic oscillations of the relativistic pendulum with friction, Phys. Lett. A, 372 (2008), 6386–6387. doi: 10.1016/j.physleta.2008.08.060.
|
|
[29]
|
P. J. Torres, Nondegeneracy of the periodically forced Liénard differential equation with Φ-Laplacian, Commun. Contemp. Math., 13 (2011), 283–292. doi: 10.1142/S0219199711004208.
|
|
[30]
|
M. Zhang, Periodic solutions of damped differential systems with repulsive singular forces, Proc. Amer. Math. Soc., 127 (1999), 401–407.
|
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