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On the oscillation of certain second order nonlinear dynamic equations. (English) Zbl 1185.34041
Summary: We establish some new oscillation criteria for solutions to the second order nonlinear dynamic equation (a(xΔ)α)Δ(t)+q(t)xβ(t)=0.
MSC:
34C15Nonlinear oscillations, coupled oscillators (ODE)
34N05Dynamic equations on time scales or measure chains
References:
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[3]Bohner, M.; Peterson, A.: Dynamic equations on time scales: an introduction with applications, (2001)
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[8]Erbe, L.; Peterson, A.; Saker, S. H.: Oscillation criteria for second-order nonlinear delay dynamic equations, J. math. Anal. appl. 333, 505-522 (2007) · Zbl 1125.34046 · doi:10.1016/j.jmaa.2006.10.055
[9]Han, Z.; Sun, S.; Shi, B.: Oscillation criteria for a class of second-order Emden–Fowler delay dynamic equations on time scales, J. math. Anal. appl. 334, 847-858 (2007) · Zbl 1125.34047 · doi:10.1016/j.jmaa.2007.01.004
[10]Hilger, S.: Analysis on measure chains – A unified approach to continuous and discrete calculus, Results math. 18, 18-56 (1990) · Zbl 0722.39001
[11]Hardy, G. H.; Littlewood, J. E.; Polya, G.: Inequalities, (1959)
[12]Agarwal, R. P.; Bohner, M.; Grace, S. R.; O’regan, D.: Discrete oscillation theory, (2005)
[13]Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for difference and functional differential equations, (2000)
[14]Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for second order linear, half-linear, superlinear and sublinear dynamic equations, (2002)
[15]Agarwal, R. P.; Grace, S. R.; O’regan, D.: Oscillation theory for second order dynamic equations, (2003)
[16]Agarwal, R. P.; Grace, S. R.; O’regan, D.: On the oscillation of certain second order difference equations, J. difference equ. Appl. 9, 109-119 (2005) · Zbl 1039.39003 · doi:10.1080/10236190290015380