Infinitely many periodic solutions for ordinary $ p(t) $-Laplacian differential systems

Chungen Liu; Yuyou Zhong; Chungen Liu; Yuyou Zhong

doi:10.3934/era.2022083

Electronic Research Archive

2022, Volume 30, Issue 5: 1653-1667. doi: 10.3934/era.2022083

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Infinitely many periodic solutions for ordinary $ p(t) $-Laplacian differential systems

Chungen Liu ^,,
Yuyou Zhong

School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

Received: 14 September 2021 Revised: 08 November 2021 Accepted: 09 December 2021 Published: 24 March 2022

In this paper, we consider the existence of infinitely many periodic solutions for some ordinary $ p(t) $-Laplacian differential systems by minimax methods in critical point theory.
- periodic solutions,
- $ p(t) $-Laplacian system,
- critical points,
- variational method
Citation: Chungen Liu, Yuyou Zhong. Infinitely many periodic solutions for ordinary $ p(t) $-Laplacian differential systems[J]. Electronic Research Archive, 2022, 30(5): 1653-1667. doi: 10.3934/era.2022083

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Abstract

In this paper, we consider the existence of infinitely many periodic solutions for some ordinary $ p(t) $-Laplacian differential systems by minimax methods in critical point theory.

References

[1]	X. L. Fan, X. Fan, A Knobloch-type result for $p(t)$-Laplacian systems, J. Math. Anal. Appl., 282 (2003), 453–464. https://doi.org/10.1016/S0022-247X(02)00376-1 doi: 10.1016/S0022-247X(02)00376-1
[2]	X. J. Wang, R. Yuan, Existence of periodic solutions for $p(t)$-Laplacian systems, Nonlinear Anal., 70 (2009), 866–880. https://doi.org/10.1016/j.na.2008.01.017 doi: 10.1016/j.na.2008.01.017
[3]	L. Zhang, P. Zhang, Periodic solutions of second-order differential inclusions systems with $p(t)$-Laplacian, Abstr. Appl. Anal., 2012 (2012), 475956. https://doi.org/10.1155/2012/475956 doi: 10.1155/2012/475956
[4]	P. Habets, R. Manasevich, F. Zanolin, A nonlinear boundary value problem with potential oscillating around the first eigenvalue, J. Differ. Equ., 117 (1995), 428–445. https://doi.org/10.1006/jdeq.1995.1060 doi: 10.1006/jdeq.1995.1060
[5]	Y. He, B. Xu, Infinitely many periodic solutions of ordinary differential equations, Appl. Math. Lett., 38 (2014), 149–154. https://doi.org/10.1016/j.aml.2014.07.018 doi: 10.1016/j.aml.2014.07.018
[6]	J. Mawhin, M. Willem, Critical point theory and Hamiltonian systems, Appl. Math. Sci., 74 (1989), Springer, New York. https://doi.org/10.1007/978-1-4757-2061-7 doi: 10.1007/978-1-4757-2061-7
[7]	X. P. Wu, C. L. Tang, Periodic solutions of a class of non-autonomous second-order systems, J. Math. Anal. Appl., 236 (1999), 227–235. https://doi.org/10.1006/jmaa.1999.6408 doi: 10.1006/jmaa.1999.6408
[8]	P. Zhang, C. L. Tang, Infinitely many periodic solutions for nonautonomous sublinear second-order Hamiltonian systems, Abstr. Appl. Anal., 2010 (2010), 620438. https://doi.org/10.1155/2010/620438 doi: 10.1155/2010/620438
[9]	C. Li, R. Agarwal, C. L. Tang, Infinitely many periodic solutions for ordinary $p$-Laplacian systems, Adv. Nonlinear Anal., 4 (2015), 251–261. https://doi.org/10.1515/anona-2014-0048 doi: 10.1515/anona-2014-0048
[10]	H. S. L$\ddot{u}$, D. O'Regan, R. P. Agarwal, On the existence of multiple periodic solutions for the vector $p$-Laplacian via critical point theory, Appl. Math., 50 (2005), 555–568. https://doi.org/10.1007/s10492-005-0037-8 doi: 10.1007/s10492-005-0037-8
[11]	X. H. Tang, X. Y. Zhang, Periodic solutions for second-order Hamiltonian systems with a $p$-Laplacian, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 64 (2010), 93–113. https://doi.org/10.2478/v10062-010-0008-8 doi: 10.2478/v10062-010-0008-8
[12]	S. N. Antontsev, S. I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions, Nonlinear Anal., 60 (2005), 515–545.
[13]	X. L. Fan, Q. H. Zhang, Existence of solutions for $p(x)$-Laplacian Dirichlet problem, Nonlinear Anal., 52 (2003), 1843–1852. https://doi.org/10.1016/S0362-546X(02)00150-5 doi: 10.1016/S0362-546X(02)00150-5
[14]	X. L. Fan, D. Zhao, On the spaces $L^{p(x)}(\Omega)$ and $W^{m, p(x)}(\Omega)$, J. Math. Anal. Appl., 263 (2001), 424–446. https://doi.org/10.1006/jmaa.2000.7617 doi: 10.1006/jmaa.2000.7617
[15]	X. L. Fan, Y. Z. Zhao, D. Zhao, Compact embedding theorems with symmetry of Strauss-Lions type for the Space $W^{1, p(x)}(\Omega)$, J. Math. Anal. Appl., 255 (2001), 333–348. https://doi.org/10.1006/jmaa.2000.7266 doi: 10.1006/jmaa.2000.7266
[16]	L. Zhang, X. H. Tang, Existence and multiplicity of periodic solutions for some second order differential systems with $p(t)$-Laplacian, Math. Slovaca, 63 (2013), 1269–1290. https://doi.org/10.2478/s12175-013-0170-x doi: 10.2478/s12175-013-0170-x

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