Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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SOLVABILITY OF A THIRD ORDER NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATION

  • Liu, Zeqing (Department of Mathematics Liaoning Normal University) ;
  • Wang, Wei (Department of Mathematics Liaoning Normal University) ;
  • Park, Jong Seo (Department of Mathematics Education Chinju National University of Education) ;
  • Kang, Shin Min (Department of Mathematics and RINS Gyeongsang National University)
  • Received : 2010.03.18
  • Accepted : 2010.06.01
  • Published : 2010.09.30
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Abstract

This work deals with the existence of uncountably many bounded positive solutions for the third order nonlinear neutral delay differential equation $$\frac{d^3}{dt^3}[x(t)+p(t)x(t-{\tau})]+f(t,x(t-{{\tau}_1}),{\ldots},x(t-{{\tau}_k}))=0,\;t{\geq}t_0$$ where ${\tau}>0$, ${\tau}_i{\in}{\mathbb{R}^+}$ for $i{\in}\{1,2,{\ldots},k\}$, $p{\in}C([t_0,+{\infty}),{\mathbb{R}^+})$ and $f{\in}C([t_0,+{\infty}){\times}{\mathbb{R}^k},{\mathbb{R}})$.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of Liaoning Province

References

  1. M. K. Grammatikopoulos, E. A. Grove and G. Ladas, Oscillations of first-order neutral delay differential equations, J. Math. Anal. Appl. 120 (1986), 510-520. https://doi.org/10.1016/0022-247X(86)90172-1
  2. M. K. Grammatikopoulos, G. Ladas and Y. G. Sficas, Oscillation and asymptotic behavior of first-order neutral equations with variable coefcients, Rad. Mat. 2 (1986), 279-303.
  3. M. R. S. Kulenovic and S. Hadziomerspahic, Existence of nonoscillatory solution of second order linear neutral delay equation, J. Math. Anal. Appl. 228 (1998), 436-448. https://doi.org/10.1006/jmaa.1997.6156
  4. G. Ladas and Y. G. Sficas, Oscillations of neutral delay differential equations, Canad. Math. Bull. 29 (1986), 438-445. https://doi.org/10.4153/CMB-1986-069-2
  5. O. Ocalan, Existence of positive solutions for a neutral differential equation with positive and negative coeficients, Appl. Math. Lett. 22 (2009), 84-90. https://doi.org/10.1016/j.aml.2008.02.009
  6. Z. Liu and S. M. Kang, Infinite many nonoscillatory solutions for second order non- linear neutral delay differential equations, Nonlinear Anal. 70 (2009), 4274-4293. https://doi.org/10.1016/j.na.2008.09.013
  7. J. S. Yu, M. P. Chen and H. Zhang, Oscillation and nonoscillation in neutral equations with integrable coeficients, Comput. Math. Appl. 35 (1998), 65-71.
  8. W. P. Zhang, W. Feng, J. Yan and J. S. Song, Existence of nonoscillatory solutions of first-order linear neutral delay differential equations, Comput. Math. Appl. 49 (2005), 1021-1027. https://doi.org/10.1016/j.camwa.2004.12.006