Skip to main content

Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations

Abstract

We are concerned with the oscillatory and nonoscillatory behavior of solutions of even-order quasilinear functional differential equations of the type, where and are positive constants, and are positive continuous functions on, and is a continuously differentiable function such that,. We first give criteria for the existence of nonoscillatory solutions with specific asymptotic behavior, and then derive conditions (sufficient as well as necessary and sufficient) for all solutions to be oscillatory by comparing the above equation with the related differential equation without deviating argument.

[123456789]

References

  1. 1.

    Kiguradze IT: On the oscillatory character of solutions of the equation. Matematicheskii Sbornik. New Series 1964, 65 (107): 172–187.

    MathSciNet  Google Scholar 

  2. 2.

    Kusano T, Lalli BS: On oscillation of half-linear functional-differential equations with deviating arguments. Hiroshima Mathematical Journal 1994,24(3):549–563.

    MathSciNet  MATH  Google Scholar 

  3. 3.

    Kusano T, Naito M: Comparison theorems for functional-differential equations with deviating arguments. Journal of the Mathematical Society of Japan 1981,33(3):509–532. 10.2969/jmsj/03330509

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Kusano T, Wang J: Oscillation properties of half-linear functional-differential equations of the second order. Hiroshima Mathematical Journal 1995,25(2):371–385.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Mahfoud WE: Comparison theorems for delay differential equations. Pacific Journal of Mathematics 1979,83(1):187–197.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Tanigawa T: Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations. Hiroshima Mathematical Journal 2003,33(3):297–316.

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Tanigawa T: Oscillation criteria for a class of higher order nonlinear differential equations. Memoirs on Differential Equations and Mathematical Physics 2006, 37: 137–152.

    MathSciNet  MATH  Google Scholar 

  8. 8.

    Tanigawa T, Fentao W: On the existence of positive solutions for a class of even order quasilinear differential equations. Advances in Mathematical Sciences and Applications 2004,14(1):75–85.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Wang J: Oscillation and nonoscillation theorems for a class of second order quasilinear functional-differential equations. Hiroshima Mathematical Journal 1997,27(3):449–466.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Tomoyuki Tanigawa.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Manojlović, J., Tanigawa, T. Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations. J Inequal Appl 2006, 42120 (2006). https://doi.org/10.1155/JIA/2006/42120

Download citation

Keywords

  • Differential Equation
  • Continuous Function
  • Positive Constant
  • Asymptotic Behavior
  • Differentiable Function
\