Research article

Positive periodic solution for third-order singular neutral differential equation with time-dependent delay

  • Received: 19 July 2020 Accepted: 07 September 2020 Published: 15 September 2020
  • MSC : 34B16, 34B18, 34C25

  • In this paper, we investigate a class of third-order singular neutral differential equations with time-dependent delay. Applying Krasnoselskiios fixed point theorem, we prove the existence results of a positive periodic solution for this neutral equation.

    Citation: Yun Xin, Hao Wang. Positive periodic solution for third-order singular neutral differential equation with time-dependent delay[J]. AIMS Mathematics, 2020, 5(6): 7234-7251. doi: 10.3934/math.2020462

    Related Papers:

  • In this paper, we investigate a class of third-order singular neutral differential equations with time-dependent delay. Applying Krasnoselskiios fixed point theorem, we prove the existence results of a positive periodic solution for this neutral equation.


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    [1] R. Agarwal, S. Grace, D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer Acasemic, 2000.
    [2] A. Ardjouni, A. Djoudi, Existence, uniqueness and positivity of solutions for a neutral nonlinear periodic differential equation, Comput. Appl. Math., 34 (2015), 17-27.
    [3] T. Candan, Existence of positive periodic solutions of first order neutral differential equations with variable coefficients, Appl. Math. Lett., 52 (2016), 142-148. doi: 10.1016/j.aml.2015.08.014
    [4] Z. Cheng, Q. Yuan, Damped superlinear Duffing equation with strong singularity of repulsive type, J. Fixed Point Theory Appl., 22 (2020), 1-18. doi: 10.1007/s11784-019-0746-3
    [5] Z. Cheng, F. Li, Weak and strong singularities for second-order nonlinear differential equations with a linear difference operator, J. Fixed. Point Theory Appl., 21 (2019), 1-23. doi: 10.1007/s11784-018-0638-y
    [6] Z. Cheng, F. Li, S. Yao, Positive solutions for second-order neutral differential equations with time-dependent deviating arguments, Filomat, 33 (2019), 3627-3638. doi: 10.2298/FIL1912627C
    [7] Z. Cheng, F. Li, Positive periodic solutions for a kind of second-order neutral differential equations with variable coefficient and delay, Mediterr. J. Math., 15 (2018), 1-19. doi: 10.1007/s00009-017-1047-y
    [8] W. Cheung, J. Ren, W. Han, Positive periodic solution of second-order neutral functional differential equations, Nonlinear Anal., 71 (2009), 3948-3955. doi: 10.1016/j.na.2009.02.064
    [9] J. Chu, P. Torres, M. Zhang, Periodic solution of second order non-autonomous singular dynamical systems, J. Differ. Equations, 239 (2007), 196-212. doi: 10.1016/j.jde.2007.05.007
    [10] J. Chu, Z. Zhou, Positive solutions for singular non-linear third-order periodic boundary value problems, Nonlinear Anal. Theor., 64 (2006), 1528-1542. doi: 10.1016/j.na.2005.07.005
    [11] B. Du, Y. Liu, I. Abbas, Existence and asymptotic behavior results of periodic solution for discrete-time neutral-type neural networks, J. Franklin Inst., 353 (2016), 448-461. doi: 10.1016/j.jfranklin.2015.11.013
    [12] A. Fonda, R. Manásevich, F. Zanolin, Subharmonics solutions for some second order differential equations with singularities, SIAM J. Math. Anal., 24 (1993), 1294-1311. doi: 10.1137/0524074
    [13] R. Hakl, P. Torres, On periodic solutions of second-order differential equations with attractive-repulsive singularities, J. Differ. Equations, 248 (2010), 111-126. doi: 10.1016/j.jde.2009.07.008
    [14] L. Lv, Z. Cheng, Positive periodic solution to superlinear neutral differential equation with time-dependent parameter, Appl. Math. Lett., 98 (2019), 271-277. doi: 10.1016/j.aml.2019.06.024
    [15] R. Ma, R. Chen, Z. He, Positive periodic solutions of second-order differential equations with weak singularities, Appl. Math. Comput., 232 (2014), 97-103.
    [16] J. Ren, Z. Cheng, S. Siegmund, Neutral operator and neutral differential equation, Abst. Appl. Anal., 2011 (2011), 1-22.
    [17] J. Ren, S. Siegmund, Y. Chen, Positive periodic solutions for third-order nonlinear differential equations, Electron. J. Differ. Eq., 66 (2011), 1-19.
    [18] P. Torres, Weak singularities may help periodic solutions to exist, J. Differ. Equations, 232 (2007), 277-284. doi: 10.1016/j.jde.2006.08.006
    [19] D. Wang, Positive periodic solutions for a nonautonomous neutral delay prey-predator model with impulse and Hassell-Varley type functional response, P. Am. Math. Soc., 142 (2014), 623-638.
    [20] H. Wang, Positive periodic solutions of singular systems with a parameter, J. Differ. Equations, 249 (2010), 2986-3002. doi: 10.1016/j.jde.2010.08.027
    [21] Z. Wang, T. Ma, Existence and multiplicity of periodic solutions of semilinear resonant Duffing equations with singularities, Nonlinearity, 25 (2012), 279-307. doi: 10.1088/0951-7715/25/2/279
    [22] J. Wu, Z. Wang, Two periodic solutions of second-order neutral functional differential equations, J. Math. Anal. Appl., 329 (2007), 677-689. doi: 10.1016/j.jmaa.2006.06.084
    [23] T. Xiang, R. Yuan, Existence of periodic solutions for p-Laplacian neutral functional equation with multiple deviating arguments, Topol. Method. Nonlinear Anal., 37 (2011), 235-258.
    [24] Y. Xin, H. Liu, Singularity problems to fourth-order Rayleigh equation with time-dependent deviating argument, Adv. Differ. Equ., 368 (2018), 1-15.
    [25] Y. Xin, H. Liu, Existence of periodic solution for fourth-order generalized neutral p-Laplacian differential equation with attractive and repulsive singularities, J. Inequal. Appl., 259 (2018), 1-18.
    [26] S. Yao, J. Liu, Study on variable coefficients singular differential equation via constant coefficients differential equation, Bound. Value Probl., 3 (2019), 1-24.
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