Periodic solutions for a neutral functional differential equation with multiple variable lags
Guo, Cheng-Jun ; Wang, Gen Qiang ; Cheng, Sui-Sun
Archivum Mathematicum, Tome 042 (2006), p. 1-10 / Harvested from Czech Digital Mathematics Library

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form \[ x^{\prime }\left( t\right) +cx^{\prime }\left( t-\tau \right) =A\left( t,x(t)\right) x\left( t\right) +f\left( t,x\left( t-r_{1}\left( t\right) \right) ,\dots ,x\left( t-r_{k}\left( t\right) \right) \right) . \]

Publié le : 2006-01-01
Classification:  34K13,  47H10,  47N20
@article{107976,
     author = {Cheng-Jun Guo and Gen Qiang Wang and Sui-Sun Cheng},
     title = {Periodic solutions for a neutral functional differential equation with multiple variable lags},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {1-10},
     zbl = {1164.34517},
     mrnumber = {2227107},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107976}
}
Guo, Cheng-Jun; Wang, Gen Qiang; Cheng, Sui-Sun. Periodic solutions for a neutral functional differential equation with multiple variable lags. Archivum Mathematicum, Tome 042 (2006) pp. 1-10. http://gdmltest.u-ga.fr/item/107976/

Li L. M. Periodic solution for a class of higher dimensional nonautonomous system, Acta Math. Appl. Sinica 12(3)(1989), 272–280. (1989) | MR 1033579

Wang K. Periodic solutions to a class differential equations with deviating argument, Acta Math. Sinica 37(3)(1994), 409–413. (1994) | MR 1289267

Wang Q. Y. Existence, uniqueness and stability of periodic solutions, Chinese Ann. Mathematics 15A(5)(1994), 537–545. (1994) | MR 1332635 | Zbl 0817.34025

Tang Y. B. Periodic solutions of a class of neutral type functional differential equation, Acta Math. Appl. Sinica, 23(3)(2000), 321–328. | MR 1797627

Wang G. Q.; Cheng S. S. A priori bounds for periodic solutions of a delay Rayleigh equation, Appl. Math. Lett. 12(1999), 41–44. (1999) | MR 1749731 | Zbl 0980.34068

Wang G. Q.; Yan J. R. Existence of periodic solutions for $n$-th order nonlinear delay differential equation, Far East J. Appl. Math. 3(1999), 129–134. (1999)

Wang G. Q.; Cheng S. S. A priori bounds for periodic solutions of a delay Rayleigh equation with damping, Tamkang J. Math. 34(3)(2003), 293–298. | MR 2002244 | Zbl 1051.34057

Wang G. Q.; Yan J. R. Existence theorem of periodic positive solutions for the Rayleigh equation of retarded type, Portugaliae Math. 57(3)(2000), 153–160. | MR 1759811 | Zbl 0963.34069

Wang G. Q.; Yan J. R. Existence of periodic solutions for second order nonlinear neutral delay equations, Acta Math. Sinica 47(2)(2004), 370–384. | MR 2074362

Gaines R. E.; Mawhin J. L. Coincidence degree and nonlinear differential equations, Lecture Notes in Math. 568, Springer, 1977. (1977) | MR 0637067 | Zbl 0339.47031

Reissig R.; Sasone G.; Conti R. Nonlinear equations of higher order, Noordhoff Inter. Pub. Leyden, 1974. (1974)

Vidyasagar M. Nonlinear system analysis, Prentice Hall Inc., 1978. (1978)