Oscillation Criteria for Nonlinear Neutral Perturbed Dynamic Equations on Time Scales

Yu, Xiangbin; Sun, Hongkai; Yang, Hongyu; Jing, Haibin

doi:10.1007/978-3-642-34041-3_43

Cited by 1 publication

(2 citation statements)

References 6 publications

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“…, t ∈ T . We note that in all the above results the conditions 0 ( ) 1 c t ≤ < , 1 [6][7][8][9][10][11][13][14][15][16][17]. Also, we give some examples to illustrate the main results.…”

Section: Introductionmentioning

confidence: 79%

“…wi-dely used to study population in biological communities, electric circuit and so on [3]. In recent years, there has been much research activity concerning the oscillation and nonoscillation of solutions of some dynamic equations on time scales, and we refer the reader to the papers [4][5][6][7][8][9][10][11][12][13][14][15][16][17] and references cited therein. Regarding neutral dynamic equations, Argarwal et al [6] where 0 γ > is an odd positive integer, τ and δ are position constants, ( ) 0 t α Δ > , and proved that the oscillation of (1) is equivalent to the oscillation of a first order delay dynamic inequality.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Oscillation Criteria for Second Order Nonlinear Neutral Perturbed Dynamic Equations on Time Scales

Yu¹,

Du²,

Yang³

2013

JCP

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To investigate the oscillatory and asymptotic behavior for a certain class of second order nonlinear neutral perturbed dynamic equations on time scales. By employing the time scales theory and some necessary analytic techniques, and introducing the class of parameter functions and generalized Riccati transformation, some new sufficient conditions for oscillation of such dynamic equations on time scales were established. The results not only improve and extend some known results in the literature, but also unify the oscillation of second order nonlinear neutral perturbed differential equations and second order nonlinear neutral perturbed difference equations. In particular, the results are essentially new under the relaxed conditions for the parameter function. Some examples are given to illustrate the main results. Dynamic equations on time scales are widely used in many fields such as computer, electrical engineering, population dynamics, and neural network, etc.

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