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Research Article Open access CC BY 3.0

Oscillation Criteria for the Solutions of Higher Order Functional Dierence Equations of Neutral type

Radhanath Rath, Ajit kumar Bhuyan, B.L.S. Barik

Journal of Advances in Mathematics and Computer Science · pp. 330–340 · Published 30 Apr 2013

10.9734/BJMCS/2013/3481

Abstract

In this paper, necessary and sufficient conditions are obtained so that the neutral functional difference equation $$\Delta^{m}\big(y_n-y_{\tau(n)}\big) + q_nG(y_{\sigma(n)})=f_n,\quad n\geq n_0,$$ admits a positive bounded solution, where $$m \geq 1$$ is an odd integer, $$\Delta$$ is the forward difference operator given by $$\Delta y_n = y_{n+1}-y_n$$; $$\{f_n\}$$, $$\{q_n\}$$, are sequences of real numbers with $$q_n \geq 0$$, $$G \in C(\mathbb{R},\mathbb{R}).$$ The results of this paper improve and extend some recent work [6,15].

Asymptotic behavior dierence equation oscillatory solution non oscillatory solution

References (12)

  1. 1 Oscillation Theory of Delay Differential Equations: With Applications
  2. 2 Difference Equations: An Introduction with Applications
  3. 3 Mathematical analysis
  4. 4 Oscillation results for higher order nonlinear neutral delay difference equations [DOI]
  5. 5 On Oscillation and Asymptotic Behaviour of a Higher Order Functional Difference Equation of Neutral Type
  6. 6 Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero [DOI]
  7. 7 Asymptotic behavior in neutral difference equations with variable coefficients and more than one delay arguments
  8. 8 OSCILLATORY AND ASYMPTOTIC BEHAVIOUR OF A HOMOGENEOUS NEUTRAL DELAY DIFFERENCE EQUATION OF SECOND ORDER
  9. 9 Oscillation of Some Fourth-Order Difference Equations
  10. 10 Oscillation and non-oscillation criteria for a neutral delay difference equation of first order
  11. 11 Difference Equations and Inequalities [DOI]
  12. 12 Oscillation Theory for Functional Differential Equations [DOI]

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