Periodic solutions for a higher-order p-Laplacian neutral differential equation with multiple deviating arguments
DOI:
https://doi.org/10.5269/bspm.51390Resumen
In this article, we consider the following high-order p-Laplacian neutral differential equation with multiple deviating arguments:
$$(\varphi_{p}(x(t)-cx(t-r))^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-\tau_{1}(t)),...,x(t-\tau_{k}(t)))+e(t).$$
By appling the continuation theorem, theory of Fourier series, Bernoulli numbers theory and some analytic techniques, sufficient conditions for the existence of periodic solutions are established.
Referencias
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8. Lijun. Pan,periodic solutions for higher order differential equation with a deviating argument, J. Math. Anal. Appl 343 (2008) 904-918.
9. Xiaojing Li,Existence and uniqueness of periodic solutions for a kind of high-order p-Laplacian Duffing differential equation with sign-changing coefficient ahead of linear term. Nonlinear Analysis 71 (2009) 2764-2770
10. Liang Feng, Guo Lixiang, Lu Shiping,Existence of periodic solutions for a p-Laplacian neutral functional differential equation, Nonlinear Analysis 71(2009)427-436.
11. Lu, S, Ge, W,Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Anal., Theory Methods Appl. 56, 501-514 (2004)
12. R.E. Gaines, J.L. Mawhin ,Coincidence Degree and Nonlinear Differential Equations, Springer Verlag, Berlin, 1977.
13. M. Zhang,Nonuniform non-resonance at the first eigenvalue of the p-Laplacian, Nonlinear Anal 29(1997)41-51.
14. C. Zhong, X. Fan, W. Chen,Introduction to Nonlinear Functional Analysis [M], Lanzhou University Press, Lan Zhou, 2004 (in Chinese).
15. W. Cheug, J.L. Ren,Periodic solutions for p-Laplacian type Rayleigh equations, Nonlinear Anal.65(2006)2003-2012.
16. Xiaojing Li, Shiping Lu,Periodic solutions for a kind of high-order p-Laplacian differential equation with sign-changing coefficient ahead of the non-linear term. Nonlinear Analysis 70 (2009) 1011-1022.
17. Kai Wang, Yanling Zhu,Periodic solutions for a fourth-order p-Laplacian neutral functional differential equation Journal of the Franklin Institute 347(2010)1158-1170
2. B. Liu, L. Huang,Existence and uniqueness of periodic solutions for a kind of Lienard equation with a deviating argument, Appl. Math. Lett. 21 (2008) 56-62.
3. Aomar Anane, Omar Chakrone, Loubna Moutaouekkil,Periodic solutions for p-laplacian neutral functional differential equations with multipledeviating arguments, Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 148, pp. 1-12.
4. Aomar Anane, Omar Chakrone, Loubna Moutaouekkil,Li'enard type p-laplacian neutral rayleigh equation with a deviating argument, Electronic Journal of Differential Equations, Vol. 2010(2010), No. 177, pp. 1-8.
5. Shiping Lu,Periodic solutions to a second order p-Laplacian neutral functional differential system, Nonlinear Analysis 69 (2008) 4215-4229
6. Aomar Anane, Omar Chakrone, Loubna Moutaouekkil,Existence of periodic solution for p-Laplacian neutral Rayleigh equation with sign-variable coefficient of non linear term, International Journal of Mathematical Sciences 2013 7(2)
7. Liang Feng, Guo Lixiang, Lu Shiping,Existence of periodic solutions for a p-Laplacian neutral functional differential equation, Nonlinear Analysis 71(2009)427-436.
8. Lijun. Pan,periodic solutions for higher order differential equation with a deviating argument, J. Math. Anal. Appl 343 (2008) 904-918.
9. Xiaojing Li,Existence and uniqueness of periodic solutions for a kind of high-order p-Laplacian Duffing differential equation with sign-changing coefficient ahead of linear term. Nonlinear Analysis 71 (2009) 2764-2770
10. Liang Feng, Guo Lixiang, Lu Shiping,Existence of periodic solutions for a p-Laplacian neutral functional differential equation, Nonlinear Analysis 71(2009)427-436.
11. Lu, S, Ge, W,Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear Anal., Theory Methods Appl. 56, 501-514 (2004)
12. R.E. Gaines, J.L. Mawhin ,Coincidence Degree and Nonlinear Differential Equations, Springer Verlag, Berlin, 1977.
13. M. Zhang,Nonuniform non-resonance at the first eigenvalue of the p-Laplacian, Nonlinear Anal 29(1997)41-51.
14. C. Zhong, X. Fan, W. Chen,Introduction to Nonlinear Functional Analysis [M], Lanzhou University Press, Lan Zhou, 2004 (in Chinese).
15. W. Cheug, J.L. Ren,Periodic solutions for p-Laplacian type Rayleigh equations, Nonlinear Anal.65(2006)2003-2012.
16. Xiaojing Li, Shiping Lu,Periodic solutions for a kind of high-order p-Laplacian differential equation with sign-changing coefficient ahead of the non-linear term. Nonlinear Analysis 70 (2009) 1011-1022.
17. Kai Wang, Yanling Zhu,Periodic solutions for a fourth-order p-Laplacian neutral functional differential equation Journal of the Franklin Institute 347(2010)1158-1170
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2022-12-23
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