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Classification of nonoscillatory solutions of second order self-adjoint neutral difference equations

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Abstract

Consider the second order self-adjoint neutral difference equation of form

$$\Delta (a_n |\Delta (x_n - p_n x_{\tau _n } )|^\alpha sgn\Delta (x_n - p_n x_{\tau _n } )) + f(n,x_{g_n } ) = 0$$

In this paper, we will give the classification of nonoscillatory solutions of the above equation; and by the fixed point theorem, we present some existence results for some kinds of nonoscillatory solutions of the equation.

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Authors and Affiliations

  1. College of Mathematics and Information of Science, Hebei Normal University, 050016, Shijiazhuang, P. R. China

    Zhaoshuang Liu

Authors
  1. Yujun Liu
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  2. Zhaoshuang Liu
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  3. Zhenguo Zhang
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Additional information

Zhenguo Zhang awarded his BS from Nankai University and M. Sc. at Hebei Normal university. Since 1981 he has been at HeBei Normal university, which entitled him a professor of Mathematics and doctorial supervisor. He is a Secretary general of Differential Equation Committee of HeBei Mathematics Society. His research is supported by the National Natural Science Foundation of China and the Natural Science of HeBei Province. His research interest centers on the stability and oscillation of the functional differential equations and difference equations.

Yujun Liu is one graduate student of Prof. Zhang zhenguo. He awarded his BS in 1991 from College of Mathematics and Information of Science of HeBei Normal University. He is studying the stability and oscillation of the functional differential equations and difference equations.

Zhaoshuang Liu is a graduate student of Prof. Zhang zhenguo. She awarded her BS from College of Mathematics and Information of Science of HeBei Normal University in 2002. She is studying for a doctorate now. Her research interests center on the behavior of solutions of the functional differential equations and difference equations.

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Liu, Y., Liu, Z. & Zhang, Z. Classification of nonoscillatory solutions of second order self-adjoint neutral difference equations. JAMC 14, 237–249 (2004). https://doi.org/10.1007/BF02936111

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  • DOI: https://doi.org/10.1007/BF02936111

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