Oscillation of Solutions of Nonlinear Difference Equation With a Super-linear Neutral Term

Dharuman, C.; Thandapani, E.

doi:10.1515/msds-2018-0004

Cited by 8 publications

(12 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we present some new oscillation criteria for the equation (1.1). The obtained results simplifies the known results in the literature in the sense that we need only one condition instead of two conditions required in [7,9,11] for the oscillation of all solutions of equation (1.1). Further the results presented in this paper extend and generalize the results known [4][5][6][15][16][17][18] for the case 0 < α < 1 to the case α > 1.…”

Section: Resultssupporting

confidence: 68%

“…for the case 0 < α ≤ 1. In [7,9], the authors investigated the oscillatory behavior of equation (1.1) when α > 1, under the assumptions (1.2) and (1.3), respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In view of the above observations our aim in this paper is to present some new sufficient conditions which ensure that all solutions of equation (1.1) when the condition (1.3) holds and our results are different from that of [7,9]. For related results concerning second order differential equations with sublinear or superlinear neutral terms, we refer the reader to [3,8,13,14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Oscillation of second order nonlinear difference equations with super-linear neutral term

Ayyappan¹,

Nithyakala²

2019

Malaya J. Mat

View full text Add to dashboard Cite

show abstract

Section: Resultssupporting

confidence: 68%

“…for the case 0 < α ≤ 1. In [7,9], the authors investigated the oscillatory behavior of equation (1.1) when α > 1, under the assumptions (1.2) and (1.3), respectively.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Oscillation of second order nonlinear difference equations with super-linear neutral term

Ayyappan¹,

Nithyakala²

2019

Malaya J. Mat

View full text Add to dashboard Cite

show abstract

“…In the few decades, there has been an increased interest in the oscillatory behaviour of the solutions of the special case

double-struckT = double-struckR

of Equation . For more details, we refer to the interested readers to see the papers() and references cited therein. In addition, Zhu and Lian have considered higher order nonlinear delay neutral dynamic equations on timescales

{false(x false(t false) + P false(t false) x false(τ false(t false) false) false)}^{Δ^{m}} + true \sum_{i = 1}^{k} p_{i} false(t false) f_{i} false(x false(τ_{i} false(t false) false) false) = q false(t false)

and studied the existence of nonoscillatory solutions of it.…”

Section: Resultsmentioning

confidence: 99%

“…In the few decades, there has been an increased interest in the oscillatory behaviour of the solutions of the special case T = R of Equation 71. For more details, we refer to the interested readers to see the papers [30][31][32][33] and references cited therein. In addition, Zhu and Lian 34 have considered higher order nonlinear delay neutral dynamic equations on timescales…”

Section: Forced Nonlinear Neutral Dynamic Equationmentioning

confidence: 99%

Oscillation for a nonlinear neutral dynamic equations on time‐scales with variable exponents

Negi

Abbas

Malik

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In the present manuscript, we study the oscillation theory for a first‐order nonlinear neutral dynamic equations on timescales with variable exponents of the form false(xfalse(σfalse(tfalse)false)−Rfalse(tfalse)xξfalse(t−ηfalse)false)Δ+Tfalse(tfalse)true∏m=1nfalse|fmfalse(xfalse(t−τmfalse)false)|αmfalse(tfalse)signfalse(xfalse(t−τmfalse)false)=0,2em∀0.1emt∈false[t∗,∞false)T, where ξ is a quotient of odd positive integers; t∗∈double-struckT be a fixed number; false[t∗,∞false)T is a timescale interval; η,τm > 0; fm∈Cfalse(double-struckR,double-struckRfalse) for m = 1,2,…,n such that xfmfalse(xfalse)>03.0235pt∀x∈double-struckR\false{0false};R,T∈Crdfalse(false[t∗,∞false)T,double-struckRfalse), and the variable exponents αm(t) satisfy ∑m=1nαmfalse(tfalse)=1. The principal goal of this paper is to establish some new succinct sufficient conditions for oscillation. Furthermore, we introduce a forcing term normalΞfalse(·,xfalse(·false)false)∈Crdfalse(double-struckT×double-struckR,double-struckRfalse) and then study the oscillation. Afterward, some interesting special cases are also studied to obtain similar sufficient conditions of oscillation under certain conditions. Moreover, the oscillatory behaviour of the solutions of a first‐order neutral dynamic equation on timescale with a nonlocal condition and a forced nonlinear neutral dynamic equation on time scale are studied. But the proofs are based on the prior estimates obtained in this paper. Some enthralling examples are constructed to show the effectiveness of our analytic results. These counterparts are quite different in the literature even when double-struckT=double-struckR. Finally, the Kamenev‐type and Philos‐type oscillation criterions are established.

show abstract

Oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term

Grace

Chhatria

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

This study introduces the oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term. The findings are obtained via utilising an integral criterion as well as a comparison theorem with the oscillatory properties of a first‐order dynamic equation. We propose novel oscillation criteria that improve, extend and simplify existing ones in the literature. The results are associated with several numerical examples.

show abstract

Oscillation of Solutions of Nonlinear Difference Equation With a Super-linear Neutral Term

Cited by 8 publications

References 0 publications

Oscillation of second order nonlinear difference equations with super-linear neutral term

Oscillation of second order nonlinear difference equations with super-linear neutral term

Oscillation for a nonlinear neutral dynamic equations on time‐scales with variable exponents

Oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term

Contact Info

Product

Resources

About