Periodic solutions for a class of conservative Liénard-type equations

Emily R. Korfanty; Ankai Liu; Wenying Feng

doi:10.1051/fopen/2019003

All issues

Volume 2 (2019)

4open, 2 (2019) 5

References

Difference & Differential Equations and Applications

Open Access

Issue		4open Volume 2, 2019 Difference & Differential Equations and Applications


Article Number		5
Number of page(s)		15
Section		Mathematics - Applied Mathematics
DOI		https://doi.org/10.1051/fopen/2019003
Published online		25 April 2019

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Tiantian M, Wang Z (2011), Periodic solutions of some second-order differential equations with desultorily sublinear nonlinearities. Nonlinear Anal 74, 41–49. [CrossRef] [Google Scholar]
Wang Y, Dai X (2009), New results on existence of asymptotically stable periodic solutions of a forced Liénard type equation. Results Math 54, 359–375. [CrossRef] [Google Scholar]
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Zheng D, Zaihong W (2007), Periodic solutions of sublinear Liénard differential equations. J Math Anal Appl 330, 1478–1487. [CrossRef] [Google Scholar]
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Qiu J (2012), Positive solutions for a nonlinear periodic boundary-value problem with a parameter. Electron J Differ Equ 133, 1–10. [Google Scholar]
Xin Y, Han X, Cheng Z (2014), Existence and uniqueness of positive periodic solution for Ф-Laplacian Liénard equation. Boundary Value Problems 244, 1–11. [Google Scholar]
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Raman A, Bajaj AK, Davies P (1996), On the slow transition across instabilities in non-linear dissipative systems. J Sound Vib 192, 4, 835–865. [CrossRef] [Google Scholar]
Ye ZM (1997), The non-linear vibration and dynamic instability of thin shallow shells. J Sound Vib 202, 3, 303–311. [CrossRef] [Google Scholar]
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Feng W (2000), Decomposition conditions for two-point boundary value problems. Int J Math Math Sci 24, 6, 389–401. [CrossRef] [Google Scholar]
Lu S, Wang Y, Guo Y (2017), Existence of periodic solutions of a Liénard equation with a singularity of repulsive type. Bound Value Probl 95, 1–10. [Google Scholar]

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[1] Zhang L, Wang Y (2010), A note on periodic solutions of a forced Liénard-type equation. Anziam J 51, 350–368. [CrossRef] [Google Scholar]

[2] Zhang M (1996), Periodic solutions of Liénard equations with singular forces of repulsive type. J Math Anal Appl 203, 254–269. [CrossRef] [Google Scholar]

[3] Liénard A (1928), Etude des oscillations entretenues. Revue générale de l’électricité 23, 901–912, 946–954. [Google Scholar]

[4] Tiantian M, Wang Z (2011), Periodic solutions of some second-order differential equations with desultorily sublinear nonlinearities. Nonlinear Anal 74, 41–49. [CrossRef] [Google Scholar]

[5] Wang Y, Dai X (2009), New results on existence of asymptotically stable periodic solutions of a forced Liénard type equation. Results Math 54, 359–375. [CrossRef] [Google Scholar]

[6] Zaihong W (2001), Periodic solutions of Liénard differential equations with subquadratic potential conditions. J Math Anal Appl 256, 127–141. [CrossRef] [Google Scholar]

[7] Wang Z (2002), Existence and multiplicity of periodic solutions of the second order Liénard equation with Lipschtzian condition. Nonlinear Anal 49, 1049–1064. [CrossRef] [Google Scholar]

[8] Zheng D, Zaihong W (2007), Periodic solutions of sublinear Liénard differential equations. J Math Anal Appl 330, 1478–1487. [CrossRef] [Google Scholar]

[9] Meng J (2009), Positive periodic solutions for Liénard type p-Laplacian equations. Electron J. Differ. Equ. Paper No. 39, 1–7. [Google Scholar]

[10] Qiu J (2012), Positive solutions for a nonlinear periodic boundary-value problem with a parameter. Electron J Differ Equ 133, 1–10. [Google Scholar]

[11] Xin Y, Han X, Cheng Z (2014), Existence and uniqueness of positive periodic solution for Ф-Laplacian Liénard equation. Boundary Value Problems 244, 1–11. [Google Scholar]

[12] Ding T (1991), On periodic solutions of sublinear duffing equations. J Math Anal Appl 158, 316–332. [CrossRef] [Google Scholar]

[13] Zamora M (2017), A note on the periodic solutions of a Mathieu-Duffing type equations. Math Nachr 290, 7, 1113–1118. [CrossRef] [Google Scholar]

[14] Faraday M (1831), On a peculiar class of acoustical figures, and on certain forms assumed by a group of particles upon vibrating elastic surfaces. Philos Trans R Soc Lond Ser B 121, 299–318. [CrossRef] [Google Scholar]

[15] Natsiavas S, Theodossiades S, Goudas I (2000), Dynamic analysis of piecewise linear oscillators with time periodic coefficients. Int J Non-Linear Mech 35, 53–68. [CrossRef] [Google Scholar]

[16] Raman A, Bajaj AK, Davies P (1996), On the slow transition across instabilities in non-linear dissipative systems. J Sound Vib 192, 4, 835–865. [CrossRef] [Google Scholar]

[17] Ye ZM (1997), The non-linear vibration and dynamic instability of thin shallow shells. J Sound Vib 202, 3, 303–311. [CrossRef] [Google Scholar]

[18] Feng W (2002), Existence for a nonlinear elliptic system at resonance. Dyn Contin Discrete Impuls Syst Ser A Math Anal 9, 69–78. [CrossRef] [Google Scholar]

[19] Mawhin J (1993), Topological methods for ordinary differential equations. Lect Notes Math 1537, 74–142. [CrossRef] [Google Scholar]

[20] Feng W, Webb JRL (1997), Solvability of m-point boundary value problems with nonlinear growth. J Math Anal Appl 212, 2, 467–480. [CrossRef] [Google Scholar]

[21] Feng W (2000), Decomposition conditions for two-point boundary value problems. Int J Math Math Sci 24, 6, 389–401. [CrossRef] [Google Scholar]

[22] Lu S, Wang Y, Guo Y (2017), Existence of periodic solutions of a Liénard equation with a singularity of repulsive type. Bound Value Probl 95, 1–10. [Google Scholar]