Geodesic
Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable coefficients
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2019), pp. 10-21.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, we study the existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable coefficients. The results are established by using the Krasnoselskii's fixed point theorem. An example is given to illustrate this work. 
@article{BASM_2019_3_a1,
     author = {Bouzid Mansouri and Abdelouaheb Ardjouni and Ahcene Djoudi},
     title = {Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable coefficients},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {10--21},
     publisher = {mathdoc},
     number = {3},
     year = {2019},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2019_3_a1/}
}
TY  - JOUR
AU  - Bouzid Mansouri
AU  - Abdelouaheb Ardjouni
AU  - Ahcene Djoudi
TI  - Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable coefficients
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2019
SP  - 10
EP  - 21
IS  - 3
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2019_3_a1/
LA  - en
ID  - BASM_2019_3_a1
ER  - 
%0 Journal Article
%A Bouzid Mansouri
%A Abdelouaheb Ardjouni
%A Ahcene Djoudi
%T Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable coefficients
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2019
%P 10-21
%N 3
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2019_3_a1/
%G en
%F BASM_2019_3_a1
Bouzid Mansouri; Abdelouaheb Ardjouni; Ahcene Djoudi. Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable coefficients. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2019), pp. 10-21. https://geodesic-test.mathdoc.fr/item/BASM_2019_3_a1/

[1] Ardjouni A., Djoudi A., “Existence of periodic solutions for a second-order nonlinear neutral differential equation with variable delay”, Palestine Journal of Mathematics, 3:2 (2014), 191–197 | MR | Zbl

[2] Ardjouni A., Djoudi A., “Existence of positive periodic solutions for a nonlinear neutral differential equations with variable delay”, Applied Mathematics E-Notes, 12 (2012), 94–101 | MR | Zbl

[3] Ardjouni A., Djoudi A., “Existence of periodic solutions for a second order nonlinear neutral differential equation with functional delay”, Electronic Journal of Qualitative Theory of Differential Equations, 2012:31 (2012), 1–9 | DOI | MR

[4] Ardjouni A., Djoudi A., “Periodic solutions for a second-order nonlinear neutral differential equation with variable delay”, Electron. J. Differential Equations, 2011:128 (2011), 1–7 | MR

[5] Ardjouni A., Djoudi A., “Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale”, Rend. Sem. Mat. Univ. Politec. Torino Vol., 68:4 (2010), 349–359 | MR | Zbl

[6] Ardjouni A., Djoudi A., Rezaiguia A., “Existence of positive periodic solutions for two types of third-order nonlinear neutral differential equations with variable delay”, Applied Mathematics E-Notes, 14 (2014), 86–96 | MR | Zbl

[7] Ardjouni A., Rezaiguia A., Djoudi A., “Existence of positive periodic solutions for fouth-order nonlinear neutral differential equations with variable delay”, Adv. Nonlinear Anal., 3:3, 157–163 | MR | Zbl

[8] Burton T. A., “Liapunov functionals, fixed points and stability by Krasnoselskii's theorem”, Nonlinear Stud., 9:2 (2002), 181–190 | MR | Zbl

[9] Burton T. A., Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006 | MR | Zbl

[10] Candan T., “Existence of positive periodic solutions of first-order neutral differential equations”, Math. Methods Appl. Sci., 40 (2017), 205–209 | DOI | MR | Zbl

[11] Candan T., “Existence of positive periodic solutions of first-order neutral differential equations with variable coefficients”, Applied Mathematics Letters, 52 (2016), 142–148 | DOI | MR | Zbl

[12] Chen F. D., “Positive periodic solutions of neutral Lotka-Volterra system with feedback control”, Appl. Math. Comput., 162:3 (2005), 1279–1302 | MR | Zbl

[13] Chen F. D., Shi J. L., “Periodicity in a nonlinear predator-prey system with state dependent delays”, Acta Math. Appl. Sin. Engl. Ser., 21:1 (2005), 49–60 | DOI | MR | Zbl

[14] Cheng Z., Ren J., “Existence of positive periodic solution for variable-coefficient third-order differential equation with singularity”, Math. Meth. Appl. Sci., 37 (2014), 2281–2289 | DOI | MR | Zbl

[15] Cheng Z., Xin Y., “Multiplicity Results for variable-coefficient singular third-order differential equation with a parameter”, Abstract and Applied Analysis, 2014 (2014), 1–10 | MR

[16] Cheng S., Zhang G., “Existence of positive periodic solutions for non-autonomous functional differential equations”, Electron. J. Differential Equations, 2001:59 (2001), 1–8 | MR

[17] Deham H., Djoudi A., “Periodic solutions for nonlinear differential equation with functional delay”, Georgian Mathematical Journal, 15:4 (2008), 635–642 | MR | Zbl

[18] Deham H., Djoudi A., “Existence of periodic solutions for neutral nonlinear differential equations withvariable delay”, Electronic Journal of Differential Equations, 2010:127 (2010), 1–8 | MR

[19] Dib Y. M., Maroun M. R., Rafoul Y. N., “Periodicity and stability in neutral nonlinear differential equations with functional delay”, Electronic Journal of Differential Equations, 2005:142 (2005), 1–11 | MR

[20] Fan M., Wang K., Wong P. J. Y., Agarwal R. P., “Periodicity and stability in periodic n-species Lotka-Volterra competition system with feedback controls and deviating arguments”, Acta Math. Sin. Engl. Ser., 19:4 (2003), 801–822 | DOI | MR | Zbl

[21] Freedman H. I., Wu J., “Periodic solutions of single-species models with periodic delay”, SIAM J. Math. Anal., 23 (1992), 689–701 | DOI | MR | Zbl

[22] Kuang Y., Delay Differential Equations with Application in Population Dynamics, Academic Press, New York, 1993 | MR

[23] Li W.G., Shen Z. H., “An constructive proof of the existence Theorem for periodic solutions of Duffng equations”, Chinese Sci. Bull., 42 (1997), 1591–1595 | MR

[24] Liu Y., Ge W., “Positive periodic solutions of nonlinear Duffing equations with delay and variable coefficients”, Tamsui Oxf. J. Math. Sci., 20 (2004), 235–255 | MR | Zbl

[25] Luo Y., Wang W., Shen J., “Existence of positive periodic solutions for two kinds of neutral functional differential equations”, Appl. Math. Lett., 21 (2008), 581–587 | DOI | MR | Zbl

[26] Nouioua F., Ardjouni A., Djoudi A., “Periodic solutions for a third-order delay differential equation”, Applied Mathematics E-Notes, 16 (2016), 210–221 | MR | Zbl

[27] Raffoul Y. N., “Positive periodic solutions in neutral nonlinear differential equations”, Electron. J. Qual. Theory Differ. Equ., 2007:16 (2007), 1–10 | DOI | MR

[28] Ren J., Siegmund S., Chen Y., “Positive periodic solutions for third-order nonlinear differential equations”, Electron. J. Differential Equations, 2011:66 (2011), 1–19 | MR

[29] Smart D. R., Fixed Points Theorems, Cambridge University Press, Cambridge, 1980 | MR

[30] Wang Q., “Positive periodic solutions of neutral delay equations”, Acta Math. Sinica (N.S.), 6 (1996), 789–795 (in Chinese) | MR

[31] Wang Y., Lian H., Ge W., “Periodic solutions for a second order nonlinear functional differential equation”, Applied Mathematics Letters, 20 (2007), 110–115 | DOI | MR | Zbl

[32] Zeng W., “Almost periodic solutions for nonlinear Duffing equations”, Acta Math. Sinica (N.S.), 13 (1997), 373–380 | DOI | MR | Zbl

[33] Zhang G., Cheng S., “Positive periodic solutions of non autonomous functional differential equations depending on a parameter”, Abstr. Appl. Anal., 7 (2002), 279–286 | DOI | MR | Zbl