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Oscillation theorems for fourth order functional differential equations

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Abstract

The authors investigate the oscillatory behavior of all solutions of the fourth order functional differential equations \(\frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})+q(t)f(x[g(t)])=0\) and \(\frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})=q(t)f(x[g(t)])+p(t)h(x[\sigma(t)])\) in the case where a −1/α(s)ds<∞. The results are illustrated with examples.

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References

  1. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory for Difference and Functional Differential Equations. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  2. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory for Second Order Linear, Half-linear, Superlinear and Sublinear Dynamic Equations. Kluwer, Dordrecht (2002)

    MATH  Google Scholar 

  3. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory for Second Order Dynamic Equations. Taylor & Francis, London (2003)

    MATH  Google Scholar 

  4. Györi, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon, Oxford (1991)

    MATH  Google Scholar 

  5. Agarwal, R.P., Grace, S.R., O’Regan, D.: On the oscillation of certain functional differential equations via comparison methods. J. Math. Anal. Appl. 286, 577–600 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Agarwal, R.P., Grace, S.R., O’Regan, D.: The oscillation of certain higher order functional differential equations. Math. Comput. Model. 37, 705–728 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Agarwal, R.P., Grace, S.R., O’Regan, D.: Nonoscillatory solutions for higher order dynamic equations. J. Lond. Math. Soc. 67, 165–179 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Agarwal, R.P., Grace, S.R., Manojlovic, J.V.: Oscillation criteria for certain fourth order nonlinear functional differential equations. Math. Comput. Model. 44, 163–187 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kusano, T., Lalli, B.S.: On oscillation of half-linear functional differential equations with deviating arguments. Hiroshima Math. J. 24, 549–563 (1994)

    MATH  MathSciNet  Google Scholar 

  10. Philos, Ch.G.: On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays. Arch. Math. 36, 168–178 (1981)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Ravi P. Agarwal.

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Grace, S.R., Agarwal, R.P. & Graef, J.R. Oscillation theorems for fourth order functional differential equations. J. Appl. Math. Comput. 30, 75–88 (2009). https://doi.org/10.1007/s12190-008-0158-9

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  • DOI: https://doi.org/10.1007/s12190-008-0158-9

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