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Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations

  • Ajit Kumar Bhuyan , Laxmi Narayan Padhy and Radhanath Rath EMAIL logo
Published/Copyright: August 4, 2021
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 71 Issue 4

Abstract

In this article, sufficient conditions are obtained so that every solution of the neutral difference equation

Δm(yn−pnL(yn−s))+qnG(yn−k)=0,

or every unbounded solution of

Δm(yn−pnL(yn−s))+qnG(yn−k)−unH(yα(n))=0,n≥n0,

oscillates, where m=2 is any integer, Δ is the forward difference operator given by Δyn = yn+1 − yn; Δmyn = Δ(Δm−1yn) and other parameters have their usual meaning. The non linear function L ∈ C (ℝ, ℝ) inside the operator Δm includes the case L(x) = x. Different types of super linear and sub linear conditions are imposed on G to prevent the solution approaching zero or ±∞. Further, all the three possible cases, pn ≥ 0, pn ≤ 0 and pn changing sign, are considered. The results of this paper generalize and extend some known results.

Keywords: Oscillatory solution; non oscillatory solution; asymptotic behavior; difference equation
MSC 2010: 39A10; 39A12

  1. (Communicated by Michal Fečkan)

Acknowledgement

The authors are very much thankful and obliged to the referees/reviewers and the editors for their various suggestions to improve the presentation of this paper.

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Received: 2020-06-03
Accepted: 2020-08-25
Published Online: 2021-08-04
Published in Print: 2021-08-26

© 2021 Mathematical Institute Slovak Academy of Sciences

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  1. Regular Papers
  2. Quasi-decompositions and quasidirect products of Hilbert algebras
  3. Residuation in finite posets
  4. On a problem in the theory of polynomials
  5. Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
  6. Mapping properties of the Bergman projections on elementary Reinhardt domains
  7. Lemniscate-like constants and infinite series
  8. On the Oscillation of second order nonlinear neutral delay differential equations
  9. Oscillation theorems for certain second-order nonlinear retarded difference equations
  10. De la Vallée Poussin inequality for impulsive differential equations
  11. Hs-Boundedness of a class of Fourier Integral Operators
  12. Dynamical behavior of a P-dimensional system of nonlinear difference equations
  13. Some inequalities for exponentially convex functions on time scales
  14. Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
  15. The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
  16. A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
  17. Simulations of nonlinear parabolic PDEs with forcing function without linearization
  18. An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
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https://doi.org/10.1515/ms-2021-0032
Keywords for this article
Oscillatory solution; non oscillatory solution; asymptotic behavior; difference equation

Articles in the same Issue

  1. Regular Papers
  2. Quasi-decompositions and quasidirect products of Hilbert algebras
  3. Residuation in finite posets
  4. On a problem in the theory of polynomials
  5. Fekete-Szegö problem for starlike functions connected with k-Fibonacci numbers
  6. Mapping properties of the Bergman projections on elementary Reinhardt domains
  7. Lemniscate-like constants and infinite series
  8. On the Oscillation of second order nonlinear neutral delay differential equations
  9. Oscillation theorems for certain second-order nonlinear retarded difference equations
  10. De la Vallée Poussin inequality for impulsive differential equations
  11. Hs-Boundedness of a class of Fourier Integral Operators
  12. Dynamical behavior of a P-dimensional system of nonlinear difference equations
  13. Some inequalities for exponentially convex functions on time scales
  14. Impact of different types of non linearity on the oscillatory behavior of higher order neutral difference equations
  15. The sine extended odd Fréchet-G family of distribution with applications to complete and censored data
  16. A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations
  17. Simulations of nonlinear parabolic PDEs with forcing function without linearization
  18. An existence level for the residual sum of squares of the power-law regression with an unknown location parameter
  19. A relationship between the category of chain MV-algebras and a subcategory of abelian groups
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