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Nonoscillation results for a class of third order nonlinear differential equations

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Abstract

Sufficient conditions for the nonoscillatory solutions of a class of third order nonlinear differential equations are presented. The results obtained generalize some criteria given by Parhi. In some special cases, some of these results contain weaker conditions.

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References

  1. Greguš M.Third Order Linear Differential Equations[M]. Dordrecht, Boston, Lancaster: D Reidel Publishing Company, 1987.

    Google Scholar 

  2. Swanson C A.Comparison and Oscillation Theory of Linear Differential Equations[M]. New York: A P, 1968.

    Google Scholar 

  3. Birkhoff G D. On solutions of the ordinary linear differential equations of the third order[J].Ann Math, 1911,12:103–127.

    Article  MathSciNet  Google Scholar 

  4. Greguš M. On some properties of the solutions of a homogeneous linear differential equation of the third order[J].Mat Fiz Casopis Slovensk Akad Vied, 1955,5:73–78.

    Google Scholar 

  5. Hanan M. Oscillation criteria for third order linear differential equations[J].Pacific J Math, 1961,11:919–944.

    MATH  MathSciNet  Google Scholar 

  6. Chilos Ch G. Oscillation and asymptotic behaviour of third order differential equations[J].Bull Inst Math Acad Sinica, 1983,11(2):141–160.

    MathSciNet  Google Scholar 

  7. Parhi N. Nonoscillation of solutions of a class of third order differential equations[J].Acta Math Hungar, 1989,54(1–2):79–88.

    Article  MATH  MathSciNet  Google Scholar 

  8. Cecchi M, Dôslá Z, Marini M. On the qualitative behaviour of solutions of thrid order differential equations[J].J Math Anal Appl, 1996,197(3):749–766.

    Article  MATH  MathSciNet  Google Scholar 

  9. Erbe L. Existence of oscillatory solutions and asymptotic behaviour for a class of third order linear differential equations[J].Pacific J Math, 1976,64(2):369–385.

    MATH  MathSciNet  Google Scholar 

  10. Heidel J W. Qualitative behaviour of solutions of a third order nonlinear differential equation[J].Pacific J Math, 1968,27:507–526.

    MATH  MathSciNet  Google Scholar 

  11. Parhi N. Nonoscillatory behaviour of solutions of nonhomogeneous third order differential equation [J].Applicable Analysis, 1981,12(4):273–285.

    MATH  MathSciNet  Google Scholar 

  12. Parhi N, Parhi S. Oscillation and nonoscillation theorems for nonhomogeneous third order differential equations[J].Bulletin Inst Math Academia Sinica, 1983,11(2):125–139.

    MATH  MathSciNet  Google Scholar 

  13. Parhi N, Parhi S. Nonoscillation and asymptotic behaviour for forced nonlinear third order differential equations[J].Bulletin Inst Math Academia Sinica, 1985,13(4):367–384.

    MATH  MathSciNet  Google Scholar 

  14. Parhi N, Parhi S. On the behaviour solutions of the differential equations (r (t) y″)′ +q (t) y′ β +p (t) y α =f(t)[J].Annales Polonici Mathematici, 1986,47(2):137–148.

    MATH  MathSciNet  Google Scholar 

  15. Parhi N, Parhi S. Qualitative behaviour of solutions of forced nonlinear third order differential equations[J].Riv. Math Univ Parma, 1987,13(4):201–210.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science, Erciyes University, 38039, Kayseri, Turkey

    Pakize Temtek

  2. Department of Mathematics, Faculty of Arts and Science, Gazi University, Teknikokullar, 06500, Ankara, Turkey

    Aydin Tiryaki

Authors
  1. Pakize Temtek
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  2. Aydin Tiryaki
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Communicated by CHIEN Wei-zang

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Temtek, P., Tiryaki, A. Nonoscillation results for a class of third order nonlinear differential equations. Appl Math Mech 23, 1170–1175 (2002). https://doi.org/10.1007/BF02437665

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  • DOI: https://doi.org/10.1007/BF02437665

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