Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales. (English) Zbl 1139.39302
Summary: We consider the equation \((r(t)(y^\Delta(t))^\gamma)^\Delta+ f(t,x(\delta(t)))=0\), \(t\in\mathbb T\), where \(y(t)= x(t)+ p(t)x(\tau(t))\) and \(\gamma\) is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments \(\tau(t)\) and \(\delta(t)\), \(t\in\mathbb T\).
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
| 39A12 | Discrete version of topics in analysis |
References:
| [1] | Agarwal RP, Bohner M, Saker SH: Oscillation of second order delay dynamic equations. to appear in The Canadian Applied Mathematics Quarterly · Zbl 1126.39003 |
| [2] | Agarwal RP, O’Regan D, Saker SH: Oscillation criteria for second-order nonlinear neutral delay dynamic equations.Journal of Mathematical Analysis and Applications 2004,300(1):203-217. 10.1016/j.jmaa.2004.06.041 · Zbl 1062.34068 · doi:10.1016/j.jmaa.2004.06.041 |
| [3] | Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358. · Zbl 0978.39001 · doi:10.1007/978-1-4612-0201-1 |
| [4] | Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348. · Zbl 1025.34001 |
| [5] | Erbe LH, Zhang BG: Oscillation of discrete analogues of delay equations.Differential and Integral Equations 1989,2(3):300-309. · Zbl 0723.39004 |
| [6] | Hilger S: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, M.S. thesis. Universität Würzburg, Würzburg; 1988. · Zbl 0695.34001 |
| [7] | Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus.Results in Mathematics 1990,18(1-2):18-56. · Zbl 0722.39001 · doi:10.1007/BF03323153 |
| [8] | Ladas G, Philos ChG, Sficas YG: Sharp conditions for the oscillation of delay difference equations.Journal of Applied Mathematics and Simulation 1989,2(2):101-111. · Zbl 0685.39004 · doi:10.1155/S1048953389000080 |
| [9] | Şahiner Y: Oscillation of second-order delay differential equations on time scales.Nonlinear Analysis 2005,63(5-7):e1073-e1080. · Zbl 1224.34294 |
| [10] | Şahiner Y, Stavroulakis IP: Oscillations of first order delay dynamic equations. to appear in Dynamic Systems and Applications · Zbl 1062.34068 |
| [11] | Zhang BG, Deng X: Oscillation of delay differential equations on time scales.Mathematical and Computer Modelling 2002,36(11-13):1307-1318. · Zbl 1034.34080 · doi:10.1016/S0895-7177(02)00278-9 |
| [12] | Zhang BG, Shanliang Z: Oscillation of second-order nonlinear delay dynamic equations on time scales.Computers & Mathematics with Applications 2005,49(4):599-609. 10.1016/j.camwa.2004.04.038 · Zbl 1075.34061 · doi:10.1016/j.camwa.2004.04.038 |
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