Skip to main content

Oscillation criteria for first-order forced nonlinear difference equations

Abstract

Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.

[123456123456]

References

  1. 1.

    Agarwal RP, Bohner M, Grace SR, O'Regan D: Discrete Oscillation Theory. Hindawi, New York; 2005:xiv+961.

    Google Scholar 

  2. 2.

    Agarwal RP, Grace SR: Forced oscillation of n th-order nonlinear differential equations. Applied Mathematics Letters 2000,13(7):53–57. 10.1016/S0893-9659(00)00076-8

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Agarwal RP, Grace SR, O'Regan D: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic, Dordrecht; 2000:viii+337.

    Google Scholar 

  4. 4.

    Agarwal RP, Wong PJY: Advanced Topics in Difference Equations, Mathematics and Its Applications. Volume 404. Kluwer Academic, Dordrecht; 1997:viii+507.

    Google Scholar 

  5. 5.

    Cecchi M, Došlá Z, Marini M: Nonoscillatory half-linear difference equations and recessive solutions. Advances in Difference Equations 2005,2005(2):193–204. 10.1155/ADE.2005.193

    Article  MathSciNet  MATH  Google Scholar 

  6. 6.

    Hardy GH, Littlewood JE, Pólya G: Inequalities, Cambridge Mathematical Library. 2nd edition. Cambridge University Press, Cambridge; 1988:xii+324.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ravi P Agarwal.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Agarwal, R.P., Grace, S.R. & Smith, T. Oscillation criteria for first-order forced nonlinear difference equations. Adv Differ Equ 2006, 062579 (2006). https://doi.org/10.1155/ADE/2006/62579

Download citation

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation
\