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Oscillation of certain difference equations. (English) Zbl 1051.39005
Summary: Some new criteria for the oscillation of difference equations of the form \[ \Delta ^2 x_n - p_n \Delta x_{n-h} + q_n | x_{g_n}| ^c \text{sgn} \;x_{g_n} = 0 \] and \[ \Delta ^i x_n + p_n \Delta ^{i-1} x_{n-h} + q_n | x_{g_n}| ^c \text{sgn} \;x_{g_n} = 0, \;i = 2,3, \] are established.
MSC:
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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References:
[1] S. R. Grace: On the oscillatory and asymptotic behavior of damped functional differential equations. Math. Japon. 36 (1991), 229-237. · Zbl 0732.34056
[2] S. R. Grace: Oscillatory and asymptotic behavior of damped functional differential equations. Math. Nachr. 142 (1989), 279-305. · Zbl 0698.34060
[3] S. R. Grace: Oscillation theorems for damped functional differential equations. Funkcial. Ekvac. 35 (1992), 261-278. · Zbl 0758.34053
[4] S. R. Grace, B. S. Lalli: Oscillation theorems for second order delay and neutral difference equations. Utilitas Math. 45 (1994), 197-211. · Zbl 0808.39005
[5] S. R. Grace, B. S. Lalli: Oscillation theorems for forced neutral difference equations. J. Math. Anal. Appl. 187 (1994), 91-106. · Zbl 0812.39002
[6] I. Györi, G. Ladas: Oscillation Theory of Delay Differential Equations with Applications. Oxford University Press, Oxford, 1991. · Zbl 0780.34048
[7] J. W. Hooker, W. T. Patula: A second order nonlinear difference equation: Oscillation and asymptotic behavior. J. Math. Anal. Appl. 91 (1983), 9-29. · Zbl 0508.39005
[8] G. Ladas, C. Qian: Comparison results and linearized oscillations for higher order difference equations. Internat. J. Math. & Math. Sci. 15 (1992), 129-142. · Zbl 0747.39002
[9] B. S. Lalli, S. R. Grace: Oscillation theorems for second order neutral difference equations. Appl. Math. Comput. 62 (1994), 47-60. · Zbl 0797.39004
[10] W. T. Patula: Growth and oscillation properties of second order linear difference equations. SIAM J. Math. Anal. 10 (1979), 55-61. · Zbl 0397.39001
[11] Ch. G. Philos: On oscillation of some difference equations. Funkcial. Ekvac. 34 (1991), 157-172. · Zbl 0734.39004
[12] F. Weil: Existence theorem for the difference equation \(y_{n+1} - 2y_n + y_{n-1} = h^2 f(y_n)\). Internat. J. Math. & Math. Sci. 3 (1990), 69-77.
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