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Nonlinear boundary value problems for first order differential equation with impulses

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Abstract

First order impulsive differential equations at fixed moments with nonlinear boundary conditions are studied. Existence theorems are presented that includes the initial value problem, the final value problem, and antiperiodic boundary problem.

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References

  1. Akhmetov, M.U., Zafer, A., Sejilova, R.D.: The control of boundary value problems for quasilinear impulsive integro-differential equations. Nonlinear Anal. 48, 271–286 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ballinger, G., Liu, X.: Permanence of population growth models with impulsive effect. Math. Comput. Model. 26, 59–72 (1997)

    Article  MathSciNet  Google Scholar 

  3. Batchelor, M.T., Baxter, R.J., O’Rourke, M.J., Yung, C.M.: Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions. J. Phys. A 28, 2759–2770 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen, L., Sun, J.: Nonlinear boundary problem of first order impulsive integro-differential equations. J. Comput. Appl. Math. 202, 392–401 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chen, L., Sun, J.: Nonlinear boundary problem of first order impulsive integro-differential equations. J. Comput. Appl. Math. 202, 392–401 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Franco, D., Nieto, J.J.: First-order impulsive ordinary differential equations with anti-periodic and nonlinear boundary conditions. Nonlinear Anal. 42, 163–173 (2000)

    Article  MathSciNet  Google Scholar 

  7. Franco, D., Nieto, J.J., Regan, D.O.: Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions. Appl. Math. Comput. 153, 793–802 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Haddad, W.M., Chellaboina, V., Nersesov, S.G., Sergey, G.: Impulsive and Hybrid Dynamical Systems. Stability, Dissipativity, and Control. Princeton University Press, Princeton (2006)

    MATH  Google Scholar 

  9. He, Z., Ze, X.: Monotone iterative technique for impulsive integro-differential equations with periodic boundary conditions. Comput. Math. Appl. 48, 73–84 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Iovane, G., Kapustyan, A.V., Valero, J.: Asymptotic behaviour of reaction-diffusion equations with non-damped impulsive effects. Nonlinear Anal. 68, 2516–2530 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jankowski, T.: First-order impulsive ordinary differential equations with advanced arguments. J. Math. Anal. Appl. 331, 1–12 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ladde, G.S., Lakshmikantham, V., Vatsala, A.S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston (1985)

    MATH  Google Scholar 

  13. Lakshmikantham, V., Bainov, D.D., Simenov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)

    MATH  Google Scholar 

  14. Li, M.L., Wang, M.S., Zhang, F.Q.: Controllability of impulsive functional differential systems in Banach spaces. Chaos Solitons Fractals 29(1), 175–181 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  15. Luo, Z., Nieto, J.J.: New results of periodic boundary value problem for impulsive integro-differential equations. Nonlinear Anal.: Theory Methods Appl. (2008, in press)

  16. Luo, Z., Shen, J., Nieto, J.J.: Antiperiodic boundary value problem for first-order impulsive ordinary differential equations. Comput. Math. Appl. 49, 253–261 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Nieto, J.J., O’Regan, D.: Variational approach to impulsive differential equations. Nonlinear Anal.: Real World Appl. (2008, in press)

  18. Nieto, J.J., Rodriguez-Lopez, R.: Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations. J. Math. Anal. Appl. 318, 593–610 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. Nieto, J.J., Rodriguez Lopez, R.: New comparison results for impulsive integro-differential equations and applications. J. Math. Anal. Appl. 328, 1343–1368 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Nieto, J.J., Rodriguez-Lopez, R.: Boundary value problems for a class of impulsive functional equations. Comput. Math. Appl. 55, 2715–2731 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  21. Qian, D., Li, X.: Periodic solutions for ordinary differential equations with sublinear impulsive effects. J. Math. Anal. Appl. 303, 288–303 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  22. Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)

    MATH  Google Scholar 

  23. Shen, J., Wang, W.: Impulsive boundary value problems with nonlinear boundary conditions. Nonlinear Anal. (2008, in press)

  24. Zavalishchin, S.T., Sesekin, A.N.: Dynamic Impulse Systems. Theory and Applications. Mathematics and Its Applications, vol. 394. Kluwer Academic, Dordrecht (1997)

    MATH  Google Scholar 

  25. Zeng, G.Z., Wang, F.Y., Nieto, J.J.: Complexity of delayed predator-prey model with impulsive harvest and Holling type-II functional response. Adv. Complex Syst. 11, 77–97 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Zhang, F.Q., Li, M.L., Yan, J.R.: Nonhomogeneous boundary value problem for first-order impulsive differential equations with delay. Comput. Math. Appl. 51(6–7), 927–936 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  27. Zhang, H., Chen, L., Nieto, J.J.: A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear Anal.: Real World Appl. 9(4), 1714–1726 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi, 044000, China

    Zhang Fengqin

  2. Department of Applied Mathematics, North University of China, Taiyuan, Shanxi, 030051, China

    Zhang Yajin

Authors
  1. Zhang Fengqin
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  2. Zhang Yajin
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Correspondence to Zhang Fengqin.

Additional information

This work is Supported by the National Sciences Foundation of China (10471040), the Sciences Foundation of Shanxi (20051010) and the Major Subject Foundation of Shanxi.

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Fengqin, Z., Yajin, Z. Nonlinear boundary value problems for first order differential equation with impulses. J. Appl. Math. Comput. 30, 397–407 (2009). https://doi.org/10.1007/s12190-008-0180-y

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  • DOI: https://doi.org/10.1007/s12190-008-0180-y

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