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An application of Schauder’s fixed point theorem to the existence of solutions of impulsively differential equations

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Abstract

In this paper the existence of solutions of a boundary value problem for impulsively differential equations that is difficult to solve by the upper and lower solution method will be proved by means of Schauder’s fixed point theorem, which improves some existing results.

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References

  1. Hu Shou-chun and V. Laksmikatham, PBVP for second order impulsive differential systems,Nonlinear Analysis, Theory, Methods and Applications,13, 1 (1989), 75–85.

    Article  MathSciNet  Google Scholar 

  2. Erbe, L. H. and Liu Xin-zhi, Existence results for boundary value problems of second order impulsive differential equations,Journal of Mathematical Analysis and Applications,149 (1990), 56–69.

    Article  MATH  MathSciNet  Google Scholar 

  3. Dong Yu-jun and Zhou Qin-de, Boundary value problems for second order impulsive differential equations,Acta Sci. Natur. Univ. Jilin 2 (1991), 13–20. (in Chinese)

    Google Scholar 

  4. Dong Yu-jun and Zhou Qin-de, Boundary value problems for impulsive differential equations,Acta Sci. Natur. Univ. Jilin,3 (1991), 1–8 (in Chinese)

    Google Scholar 

  5. Dong Yu-jun and Sun Wan-kai, On a PBVP for second order impulsive differential equations.The Collection of Papers from the Researching and Discussing Meeting of Mathematical Science, Jilin University Press, Changchun, August (1992), 199–202. (in Chinese)

    Google Scholar 

  6. Lazar, A. C., and D. E. Leach, On a nonlinear two point boundary value problem,Journal of Mathematical Analysis and Applications,26 (1969), 20–27.

    Article  MathSciNet  Google Scholar 

  7. Hartman, Philip,Ordinary Differential Equations, Second Edition, Boston, Basel, Stuttgart, Birkhauser (1982).

    Google Scholar 

  8. Cronin, Jane, Fixed points and topological degree in nonlinear analysis,Mathematical Surveys, No. 11, American Mathematical Society, Providence (1964).

    Google Scholar 

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Communicated by Lin Zong-chi

First Received July 19, 1993

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Yu-jun, D., Er-xin, Z. An application of Schauder’s fixed point theorem to the existence of solutions of impulsively differential equations. Appl Math Mech 16, 377–381 (1995). https://doi.org/10.1007/BF02456951

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  • DOI: https://doi.org/10.1007/BF02456951

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