Necessary and sufficient conditions for oscillations of first order neutral delay difference equations with constant coefficients

Murugesan, A.; Sowmiya, P.

doi:10.14419/ijams.v3i1.4462

Cited by 2 publications

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [11], Ö g ünmez et al established sufficient conditions for oscillation of all solutions of (1.1) and (1.2) when p ≡ 0, m = k, q i (n) = q i and r j (n) ≡ r j . In [8], we derived sufficient conditions for oscillation of all solutions of the equations (1.1) and (1.2) for the cases −1 < p < 0, m = k, q i (n) = q i and r j (n) = r j . The results obtained in [8] improves the results in [11]; In [9], we derived sufficient conditions for oscillation of all solutions of the equations (1.1) and (1.2) for the cases p(n) ≡ p with −1 < p < 0.…”

Section: Introductionmentioning

confidence: 99%

Oscillation conditions for first order neutral difference equations with positive and negative variable co-efficients

Murugesan¹,

Shanmugavalli²

2017

Malaya J. Mat.

View full text Add to dashboard Cite

In this article, we analysis the oscillatory properties of first order neutral difference equations with positive and negative variable coefficients of the forms$$\Delta[x(n)+p(n) x(n-\tau)]+\sum_{i=1}^m q_i(n) x\left(n-\sigma_i\right)-\sum_{j=1}^k r_j(n) x\left(n-\rho_j\right)=0 ; \quad n=0,1,2, \ldots,$$and$$\Delta[x(n)+p(n) x(n+\tau)]+\sum_{i=1}^m q_i(n) x\left(n+\sigma_i\right)-\sum_{j=1}^k r_j(n) x\left(n+\rho_j\right)=0 ; \quad n=0,1,2, \ldots,$$where $\{p(n)\}$ is a sequence of real numbers, $\left\{q_i(n)\right\}$ and $\left\{r_j(n)\right\}$ are sequences of positive real numbers, $\tau$ is a positive integer, $\sigma_i$ and $\rho_j$ are nonnegative integers, for $i=1,2, \ldots, m$ and $j=1,2, \ldots, k$. We established sufficient conditions for oscillation of solutions to above systems.

show abstract

Section: Introductionmentioning

confidence: 99%