Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Asymptotic Results for a Class of Fourth Order Quasilinear Difference Equations

  • Received : 2005.03.23
  • Published : 2006.12.23
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Abstract

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.

Keywords

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