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On the Kneser-Type Solutions for Two-Dimensional Linear Differential Systems with Deviating Arguments

Abstract

For the differential system,,, where,,, we get necessary and sufficient conditions that this system does not have solutions satisfying the condition for. Note one of our results obtained for this system with constant coefficients and delays (, where and). The inequality is necessary and sufficient for nonexistence of solutions satisfying this condition.

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References

  1. 1.

    Chanturiya TA: Specific conditions for the oscillation of solutions of linear differential equations with retarded argument. Ukrainskiĭ Matematicheskiĭ Zhurnal 1986,38(5):662–665, 681.

    MathSciNet  Google Scholar 

  2. 2.

    Koplatadze R: Monotone and oscillating solutions ofth-order differential equations with retarded argument. Mathematica Bohemica 1991,116(3):296–308.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Koplatadze R: Specific properties of solutions of differential equations with deviating argument. Ukrainskiĭ Matematicheskiĭ Zhurnal 1991,43(1):60–67.

    MathSciNet  Google Scholar 

  4. 4.

    Koplatadze R: On oscillatory properties of solutions of functional-differential equations. Memoirs on Differential Equations and Mathematical Physics 1994, 3: 179.

    MathSciNet  Google Scholar 

  5. 5.

    Ladde GS, Lakshmikantham V, Zhang BG: Oscillation Theory of Differential Equations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics. Volume 110. Marcel Dekker, New York, NY, USA; 1987:vi+308.

    Google Scholar 

  6. 6.

    Shmul'yan MG: On the oscillating solutions of a linear second order differential equation with retarding argument. Differentsial'nye Uravneniya 1995, 31: 622–629.

    MathSciNet  Google Scholar 

  7. 7.

    Skubačevskiĭ AL: The oscillatory solutions of a second order linear homogeneous differential equation with retarded argument. Differentsial'nye Uravneniya 1975, 11: 462–469, 587–588.

    MATH  Google Scholar 

  8. 8.

    Labovskiĭ SM: A condition for the nonvanishing of the Wronskian of a fundamental system of solutions of a linear differential equation with retarded argument. Differentsial'nye Uravneniya 1974, 10: 426–430, 571.

    Google Scholar 

  9. 9.

    Azbelev NV, Domoshnitsky A: On the question of linear differential inequalities—I. Differential Equations 1991,27(3):257–263. translation from Differentsial'nye Uravneniya, vol. 27, pp. 376–384, 1991 translation from Differentsial'nye Uravneniya, vol. 27, pp. 376–384, 1991

    MathSciNet  MATH  Google Scholar 

  10. 10.

    Azbelev NV, Domoshnitsky A: On the question of linear differential inequalities—II. Differential Equations 1991,27(6):641–647. translation from Differentsial'nye Uravneniya, vol. 27, pp, 923–931, 1991 translation from Differentsial'nye Uravneniya, vol. 27, pp, 923–931, 1991

    MathSciNet  MATH  Google Scholar 

  11. 11.

    Domoshnitsky A: Wronskian of fundamental system of delay differential equations. Functional Differential Equations 2002,9(3–4):353–376.

    MathSciNet  MATH  Google Scholar 

  12. 12.

    Kiguradze I, Partsvania N: On the Kneser problem for two-dimensional differential systems with advanced arguments. Journal of Inequalities and Applications 2002,7(4):453–477. 10.1155/S1025583402000231

    MathSciNet  MATH  Google Scholar 

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Correspondence to Alexander Domoshnitsky.

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Domoshnitsky, A., Koplatadze, R. On the Kneser-Type Solutions for Two-Dimensional Linear Differential Systems with Deviating Arguments. J Inequal Appl 2007, 052304 (2007). https://doi.org/10.1155/2007/52304

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Keywords

  • Differential System
  • Constant Coefficient
  • Linear Differential System
  • Deviate Argument