DOI QR코드

DOI QR Code

POSITIVE PERIODIC SOLUTIONS OF SYSTEMS OF FUNCTIONAL DIFFERENTIAL EQUATIONS

  • RAFFOUL YOUSSEF N. (Department of Mathematics University of Dayton)
  • 발행 : 2005.07.01

초록

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

키워드

참고문헌

  1. R. P. Agarwal and P. J. Y. Wong, On the existence of positive solutions of higher order difference equations, Topol. Methods Nonlinear Anal. 10 (1997) no. 2, 339-351 https://doi.org/10.12775/TMNA.1997.036
  2. S. Cheng and G. Zhang, Existence of positive periodic solutions for nonautonomous functional differential equations, Electron. J. Differential Equations 59 (2001), 1-8
  3. A. Datta and J. Henderson, Differences and smoothness of solutions for functional difference equations, Proceedings Difference Equations 1 (1995), 133-142.,
  4. P. W. Eloe, Y. Raffoul, D. Reid, and K. Yin, Positive solutions of nonlinear Functional Difference Equations, Comput. Math. Appl. 42 (2001), 639-646 https://doi.org/10.1016/S0898-1221(01)00183-3
  5. C. P. Gupta, Solvability of a three-point boundary value problem for a second order ordinary differential equation, J. Math. Anal. Appl. 168 (1997), 540-551
  6. C. P. Gupta and S. I. Trofimchuk, A sharper condition for the stability of a three- point second order boundary value problem, J. Math. Anal. Appl. 205 (1997), 586-597 https://doi.org/10.1006/jmaa.1997.5252
  7. J. Henderson and W. N. Hudson, Eigenvalue problems for nonlinear differential equations, Comm. Appl. Nonlinear Anal. 3 (1996), 51-58
  8. J. Henderson and A. Peterson, Properties of delay variation in solutions of delay difference equations, J. Differential Equations 1 (1995), 29-38
  9. J. Henderson and H. Wang, Positive solutions for nonlinear eigenvalue problems, J. Math. Anal. Appl. 208 (1997), 252-259 https://doi.org/10.1006/jmaa.1997.5334
  10. D. Jiang, J. Wei, and B. Zhang, Positive periodic solutions of functional differential equations and population models, Electron. J. Differential Equations 2002 (2002), no. 71, 1-13
  11. M. A. Krasnosel'skii, Positive solutions of operator Equations, Noordhoff, Groningen, 1964
  12. R. MA, A remark on a second order three-point boundary value problem , J. Math. Anal. Appl. 183 (1994), 518-522 https://doi.org/10.1006/jmaa.1994.1158
  13. R. M, Existence theorem for a second order three-point boundary value problem, J. Math. Anal. Appl. 212 (1997), 430-442 https://doi.org/10.1006/jmaa.1997.5515
  14. R. MA, Positive solutions for second order three-point boundary value problem, Appl. Math. Lett. 14 (2001), 193-204
  15. R. MA,, Positive solutions of a nonlinear three-point boundary-value problem, Electron. J. Differential Equations 1999 (1999), no. 34, 1-8
  16. F. Merdivenci, Two positive solutions of a boundary value problem for difference equations, J. Difference Equ. Appl. 1 (1995), 263-270 https://doi.org/10.1080/10236199508808026
  17. Y. Raffoul, Positive periodic solutions of nonlinear functional difference equations, Electron. J. Differential Equations 55 (2002), 1-8
  18. Y. Raffoul, Positive solutions of Three-Point Nonlinear Second Order Boundary Value Problem, Electron. J. Qual. Theory Differ. Equ. 15 (2002), 1-11
  19. W. Yin, Eigenvalue problems for functional differential equations, Journal of Nonlinear Differential Equations 3 (1997), 74-82

피인용 문헌

  1. Periodic solutions of a class of impulsive neutral delay differential equation vol.219, pp.8, 2012, https://doi.org/10.1016/j.amc.2012.10.031
  2. Positive periodic solutions of nonautonomous functional differential systems vol.333, pp.2, 2007, https://doi.org/10.1016/j.jmaa.2006.09.084
  3. Existence theorems for some abstract nonlinear non-autonomous systems with delays vol.19, pp.9, 2014, https://doi.org/10.1016/j.cnsns.2014.01.026