Periodic solutions for a neutral functional differential equation with multiple variable lags

Cheng-Jun Guo; Gen Qiang Wang; Sui-Sun Cheng

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 1, page 1-10
  • ISSN: 0044-8753

Abstract

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By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form x ' t + c x ' t - τ = A t , x ( t ) x t + f t , x t - r 1 t , ⋯ , x t - r k t .

How to cite

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Guo, Cheng-Jun, Wang, Gen Qiang, and Cheng, Sui-Sun. "Periodic solutions for a neutral functional differential equation with multiple variable lags." Archivum Mathematicum 042.1 (2006): 1-10. <http://eudml.org/doc/249790>.

@article{Guo2006,
abstract = {By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form \[ x^\{\prime \}\left( t\right) +cx^\{\prime \}\left( t-\tau \right) =A\left( t,x(t)\right) x\left( t\right) +f\left( t,x\left( t-r\_\{1\}\left( t\right) \right) ,\dots ,x\left( t-r\_\{k\}\left( t\right) \right) \right) . \]},
author = {Guo, Cheng-Jun, Wang, Gen Qiang, Cheng, Sui-Sun},
journal = {Archivum Mathematicum},
keywords = {neutral differential system; periodic solutions; fixed point theorem; neutral differential system; periodic solutions; fixed point theorem},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Periodic solutions for a neutral functional differential equation with multiple variable lags},
url = {http://eudml.org/doc/249790},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Guo, Cheng-Jun
AU - Wang, Gen Qiang
AU - Cheng, Sui-Sun
TI - Periodic solutions for a neutral functional differential equation with multiple variable lags
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 1
SP - 1
EP - 10
AB - By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form \[ x^{\prime }\left( t\right) +cx^{\prime }\left( t-\tau \right) =A\left( t,x(t)\right) x\left( t\right) +f\left( t,x\left( t-r_{1}\left( t\right) \right) ,\dots ,x\left( t-r_{k}\left( t\right) \right) \right) . \]
LA - eng
KW - neutral differential system; periodic solutions; fixed point theorem; neutral differential system; periodic solutions; fixed point theorem
UR - http://eudml.org/doc/249790
ER -

References

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  1. Li L. M., Periodic solution for a class of higher dimensional nonautonomous system, Acta Math. Appl. Sinica 12(3)(1989), 272–280. (1989) MR1033579
  2. Wang K., Periodic solutions to a class differential equations with deviating argument, Acta Math. Sinica 37(3)(1994), 409–413. (1994) MR1289267
  3. Wang Q. Y., Existence, uniqueness and stability of periodic solutions, Chinese Ann. Mathematics 15A(5)(1994), 537–545. (1994) Zbl0817.34025MR1332635
  4. Tang Y. B., Periodic solutions of a class of neutral type functional differential equation, Acta Math. Appl. Sinica, 23(3)(2000), 321–328. MR1797627
  5. 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) Zbl0980.34068MR1749731
  6. 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) 
  7. 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. Zbl1051.34057MR2002244
  8. 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. Zbl0963.34069MR1759811
  9. 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. MR2074362
  10. Gaines R. E., Mawhin J. L., Coincidence degree and nonlinear differential equations, Lecture Notes in Math. 568, Springer, 1977. (1977) Zbl0339.47031MR0637067
  11. Reissig R., Sasone G., Conti R., Nonlinear equations of higher order, Noordhoff Inter. Pub. Leyden, 1974. (1974) 
  12. Vidyasagar M., Nonlinear system analysis, Prentice Hall Inc., 1978. (1978) 

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