• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.477-488
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• 2006

In this paper, the authors first classify all nonoscillatory solutions of equation (1) $${\Delta}^2|{\Delta}^2{_{y_n}}|^{{\alpha}-1}{\Delta}^2{_{y_n}}+q_n|y_{{\sigma}(n)}|^{{\beta}-1}y_{{\sigma}(n)}=o,\;n{\in}\mathbb{N}$$ into six disjoint classes according to their asymptotic behavior, and then they obtain necessary and sufficient conditions for the existence of solutions in these classes. Examples are inserted to illustrate the results.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.245-256
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• 2005

We consider the second-order nonlinear difference equation (1) $$\Delta(a_nh(x_{n+1}){\Delta}x_n)+p_{n+1}f(x_{n+1})=0,\;n{\geq}n_0$$ where ${a_n},\;{p_n}$ are sequences of integers with $a_n\;>\;0,\;\{P_n\}$ is a real sequence without any restriction on its sign. hand fare real-valued functions. We obtain some necessary conditions for (1) existing nonoscillatory solutions and sufficient conditions for (1) being oscillatory.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.49-62
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• 2007

In this paper, the oscillation and existence of nonoscillatory solutions of odd order difference equations with nonlinear neutral terms are studied respectively. Some new criteria are established. Furthermore, some examples are given to illustrate the advance of our results.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.103-120
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• 2002

A second order upwind method for linear hyperbolic systems is studied in this paper. The method approximates solutions as piecewise linear functions, and state variables and slopes of the linear functions for next time step are computed separately. We present a new method for the computation of slopes, derived from an upwinding difference for a derivative. For nonoscillatory solutions, a monotonicity algorithm is also proposed by modifying an existing algorithm. To validate our second order upwind method, numerical results for linear advection equations and linear systems for elastic and acoustic waves are given.