1. M. Izydorek and J. Janczewska, Homoclinic solutions
for a class of the second order Hamiltonian systems,
J. Differential Equations 219(2), 375–389 (2005). DOI:
https://doi.org/10.1016/j.jde.2005.06.029#
2. J. Jiang, S. Lu, X. Lv, Homoclinic solutions for a class
of second order Hamiltonian systems, Nonlinear Analy
sis: Real World Applications 13, 176–185 (2012). DOI:
https://doi.org/10.1016/j.nonrwa.2011.07.0
16#
3. S. Lu, X. Lv and P. Yan, Existence of homoclinics for
a class of Hamiltonian systems, Nonlinear Analysis 72,
390–398 (2010). DOI: https://doi.org/10.1016/
j.na.2009.06.073#
4. P.H. Rabinowitz, Homoclinic orbits for a class of
Hamiltonian systems, Proc. Roy. Soc. Edinburgh 114A,
33–38 (1990). DOI: https://doi.org/10.1017/S0
308210500024240#
5. X.H. Tang, L. Xiao, Homoclinic solutions for a class of
second order Hamiltonian systems, Nonlinear Analysis
71, 1140–1152 (2009). DOI: https://doi.org/10.1
016/j.na.2008.11.039#
6. R. Yuan, Z. Zhang, Homoclinic solutions for some sec
ond order nonautonomous Hamiltonian systems with
out the globally superquadratic condition, Nonlinear
Analysis 72, 1809–1819 (2010). DOI: https://doi.
org/10.1016/j.na.2009.09.011#
7. G. Chen, Homoclinic orbits for second order Hamil
tonian systems with asymptotically linear terms at in
finity, Advances in Difference Equations 2014(114),
(2014). DOI: https://doi.org/10.1186/1687-1
847-2014-114#
8. G. Chen, Z. He, Infinitely many homoclinic solu
tions for a class of second order Hamiltonian systems,
Advances in Difference Equations 2014(161), (2014).
DOI: https://doi.org/10.1186/1687-1847-201
4-161#
9. L. Chu, Q. Zhang, Homoclinic solutions for a class of
second order Hamiltonian systems with locally defined
potentials, Nonlinear Analysis 75, 3188–3197 (2012).
DOI: https://doi.org/10.1016/j.na.2011.12
.015#
10. Y. Ding, Existence and multiplicity results for homo
clinic solutions to a class of Hamiltonian systems, Non
linear Analysis 25(11), 1095–1113 (1995). DOI: http
s://doi.org/10.1016/0362-546X(94)00156-Q#
11. X. Lin and X.H. Tang, Homoclinic solutions for a class
of second order Hamiltonian systems, J. Math. Anal.
Appl. 354, 539–549 (2009). DOI: https://doi.or
g/10.1016/j.jmaa.2008.12.048#
12. X. Lin and X.H. Tang, Infinitely many homoclinic or
bits for Hamiltonian systems with indefinite sign sub
quadratic potentials, Nonlinear Analysis 74, 6314–6325
(2011). DOI: https://doi.org/10.1016/j.na.2
011.06.038#
13. C. Liu, Q. Zhang, Infinitely many homoclinic solutions
for second order Hamiltonian systems, Nonlinear Anal
ysis 72, 894–903 (2010). DOI: https://doi.org/10
.1016/j.na.2009.07.016#
14. P.H. Rabinowitz and K. Tanaka, Some results on con
necting orbits for a class of Hamiltonian systems, Math.
Z. 206(3), 473–499 (1991). DOI: https://doi.org/
10.1007/BF02571368"
15. J. Sun, T-f. Wu, Homoclinic solutions for a second or
der Hamiltonian system with a positive semi-definite
matrix, Chaos, Solitons and Fractals 76, 24–31 (2015).
DOI: https://doi.org/10.1016/j.chaos.2015
.04.006#
16. J. Sun, T-f. Wu, Multiplicity and concentration of ho
moclinic solutions for some second order Hamilto
nian systems, Nonlinear Analysis 114, 105–115 (2015).
DOI: https://doi.org/10.1016/j.na.2014.11
.007#
17. C.L. Tang, Li-Li Wan, Existence of homoclinic orbits
for second order Hamiltonian systems without (AR)
condition, Nonlinear Analysis 74, 5303–5313 (2011).
DOI: https://doi.org/10.1016/j.na.2011.04
.067#
18. J. Wei, J. Wang, Infinitely many homoclinic orbits for
the second order Hamiltonian systems with general po
tentials, J. Math. Anal. Appl. 366(2), 694–699 (2010).
DOI: https://doi.org/10.1016/j.jmaa.2010.
01.038#
19. Z. Zhang, Existence of homoclinic solutions for second
order Hamiltonian systems with general potentials, J.
Appl. Math. Comput. 44, 263–272 (2014). DOI: http
s://doi.org/10.1007/s12190-013-0694-6#
20. R.P. Agarwal, P. Chen and X. Tang, Fast homoclinic so
lutions for a class of damped vibration problems, Ap
plied Mathematics and Computation 219, 6053–6065
(2013). DOI: https://doi.org/10.1016/j.amc.
2012.12.005#
21. P. Chen and X.H. Tang, Fast homoclinic solutions for a
class of damped vibration problems with sub-quadratic
potentials, Math. Nachr. 286(1), 4–16 (2013). DOI: ht
tps://doi.org/10.1002/mana.201100258#
22. F. Khelifi, M. Timoumi, Even homoclinic orbits for a
class of damped vibration systems, Indagationes Math
ematicae 28(6), 1111–1125 (2017). DOI: https://do
i.org/10.1016/j.indag.2017.08.001#
23. M. Timoumi, Infinitely many fast homoclinic solutions
for a class of superquadratic damped vibration systems,
Journal of Elliptic and Parabolic Equations 6, 451–471
(2020). DOI: https://doi.org/10.1007/s41808-020-00071-3#
24. M. Timoumi, On ground state homoclinic orbits of
a class of superquadratic damped vibration systems,
Mediterr. J. Math. 15, Article 214 (2018). DOI: https:
//doi.org/10.1007/s00009-018-1212-8#
25. R. Yuan and Z. Zhang, Fast homoclinic solutions for
some second order non-autonomous systems, J. Math.
Anal. Appl. 376, 51–63 (2011). DOI: https://doi.
org/10.1016/j.jmaa.2010.10.045#
