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Bounded oscillation of second order unstable neutral type difference equations

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Abstract

In this paper the authors present sufficient conditions for all bounded solutions of the second order neutral difference equation

$$\Delta ^2 (y_n - py_{n - k} ) - q_n f(y_{n - \ell } ) = 0, n \in \mathbb{N}$$

to be oscillatory. Examples are provided to illustrate the results.

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Authors and Affiliations

  1. Department of Mathematics, Periyar University, 636 011, Salem, India

    E. Thandapani

  2. Department of Mathematics, Kandaswami Kandar's College, Velur-638 182, Namakkal Dt, Tamil Nadu, India

    R. Arul & P. S. Raja

Authors
  1. E. Thandapani
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  2. R. Arul
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  3. P. S. Raja
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Corresponding author

Correspondence to E. Thandapani.

Additional information

E. Thandapani received his M. Sc., and Ph. D., from the University of Madras. He has published more than one hundred papers in the field of inequalities and oscillation theory of differential and difference equations. He is currently a Reader in the Department of Mathematics, Periyar University, Salem-636 011, India.

R. Arul received his M. Sc., and Ph. D., from the University of Madras under the guidance of Dr. E. Thandapani. He is currently a Reader in the Department of Mathematics, Kandaswami Kandar's College, Velur-638 182, Namakkal Dt, Tamil Nadu, India. His research interest centered on the oscillation of difference equation.

P. S. Raja received his M. Sc., from the University of Madras. He is currently doing Ph. D., under the guidance of Dr. R. Arul. His interest centered on qualitative properties of difference equations.

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Thandapani, E., Arul, R. & Raja, P.S. Bounded oscillation of second order unstable neutral type difference equations. JAMC 16, 79–90 (2004). https://doi.org/10.1007/BF02936152

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  • DOI: https://doi.org/10.1007/BF02936152

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