EXISTENCE AND MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS FOR A CLASS OF SECOND ORDER DAMPED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS

Ping Liu; Yonghong Fan; Linlin Wang

doi:10.11948/20190421

2021 Volume 11 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2021 > 11(2): 798-809

Next Article Previous Article

Ping Liu, Yonghong Fan, Linlin Wang. EXISTENCE AND MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS FOR A CLASS OF SECOND ORDER DAMPED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 798-809. doi: 10.11948/20190421

Citation:

Ping Liu, Yonghong Fan, Linlin Wang. EXISTENCE AND MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS FOR A CLASS OF SECOND ORDER DAMPED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 798-809. doi: 10.11948/20190421

EXISTENCE AND MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS FOR A CLASS OF SECOND ORDER DAMPED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS

1.
School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China

Corresponding author: Email address: fanyh_1993@sina.com(Y. Fan)

Abstract

Abstract

By using the Krasnoselskii fixed point theorem, sufficient conditions are obtained for the existence and multiplicity of positive periodic solutions for a class of second order damped functional differential equations with multiple delays. Our results are a further expansion of the previous research results.
- Periodic solutions /
- Green's function /
- Krasnoselskii fxed point
MSC: 35B10, 65L03

FullText(HTML)

References

[1]	Z. Cheng and F. Li, Positive periodic solutions for a kind of second-order neutral differential equations with variable coefcient and delay, Mediterr. J. Math., 2018, 15(3), 134–152. doi: 10.1007/s00009-018-1184-y CrossRef Google Scholar
[2]	J. Chu, N. Fan and P. J. Torres, Periodic solutions for second order singular damped differential equations, J. Math. Anal. Appl., 2012, 388(2), 665–675. doi: 10.1016/j.jmaa.2011.09.061 CrossRef Google Scholar
[3]	J. Chu, X. Lin, D. O. Regan et al., Multiplicity of positive solutions to second order differential equations, Bull. Austral. Math. Soc., 2006, 73(02), 175–182. doi: 10.1017/S0004972700038764 CrossRef Google Scholar
[4]	K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, New York, 1985. Google Scholar
[5]	H. Gabsi, A. Ardjouni and A. Djoudi, Existence of positive periodic solutions of nonlinear neutral differential systems with variable delays, 2018, 64, 83–97. Google Scholar
[6]	D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988. Google Scholar
[7]	R. Hakl and P. J. Torres, Maximum and antimaximum principles for a second order differential operator with variable codfcients of indefnite sign, Appl. Math. Comput., 2011, 217(19), 7599–7611. Google Scholar
[8]	J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977. Google Scholar
[9]	E. Hernández and S. Trofmchuk, Traveling waves solutions for partial neutral differential equations, Journal of Mathematical Analysis and Applications, 2020, 481(1), Article ID 123458. doi: 10.1016/j.jmaa.2019.123458 CrossRef Google Scholar
[10]	D. Jiang, J. J. Nieto and W. Zuo, On monotone method for frst and second order periodic boundary value problems and periodic solutions of functional differential equations, J. Math. Anal. Appl., 2004, 289(2), 691–699. doi: 10.1016/j.jmaa.2003.09.020 CrossRef Google Scholar
[11]	S. Kang and S. Cheng, Periodic solution for second order periodic differential equations under scalable control, Appl. Math. Comput., 2012, 218(18), 9138– 9146. Google Scholar
[12]	Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993. Google Scholar
[13]	Q. Li and Y. Li, On the existence of positive periodic solutions for second-order functional differential equations with multiple delays, Abstr. Appl. Anal., 2012, Article ID 929870. Google Scholar
[14]	B. Mansouri, A. Ardjouni and A. Djoudi, Periodicity and continuous dependence in iterative differential equations, Rendiconti del Circolo Matematico di Palermo Series 2, 2019. DOI: 10.1007/s12215-019-00420-5. CrossRef Google Scholar
[15]	M. I. Muminov, On the method of fnding periodic solutions of second-order neutral differential equations with piecewise constant arguments, Advances in Difference Equations, 2017, 336, 1–17. Google Scholar
[16]	H. V. Ngo, Existence results for extremal solutions of interval fractional functional integro-differential equations, Fuzzy Sets and Systems, 2018, 347(15), 29–53. Google Scholar
[17]	Z. Sabir, H. A. Wahab, M. Umar et al., Stochastic numerical approach for solving second order nonlinear singular functional differential equation, Applied Mathematics and Computation, 2019, 363(15), Article ID 124605. Google Scholar
[18]	P. J. Torres, Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fxed point theorem, J. Differential Equations, 2003, 190(2), 643–662. doi: 10.1016/S0022-0396(02)00152-3 CrossRef Google Scholar
[19]	C. Tunc and S. Erdur, New qualitative results for solutions of functional differential equations of second order, Discrete Dynamics in Nature and Society, 2018, DOI: 10.1155/2018/3151742. CrossRef Google Scholar
[20]	N. Wang, Existence and uniqueness of periodic solutions for a kind of secondorder neutral functional differential equation with delays, Advances in Mathematical Physics, 2017, Article ID 9591087. Google Scholar
[21]	Y. Wu, Existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter, Nonlinear Anal., 2009, 70(1), 433–443. doi: 10.1016/j.na.2007.12.011 CrossRef Google Scholar