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Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations

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Abstract

This paper considers a class of fourth order nonlinear difference equations Δ2(r n Δ2(y n ) + Δ2(r n ,f(n,n n )=0,n ∈N(n 0) wheref(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory.

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Authors and Affiliations

  1. Department of Mathematics, Shanxi University, 030006, Taiyuan, China

    Yan Jurang

  2. Department of Mathematics, Hubei Normal University, 435002, Huangshi, China

    Liu Bin

Authors
  1. Yan Jurang
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  2. Liu Bin
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Partially Supported by the National Science Foundation of China

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Jurang, Y., Bin, L. Oscillatory and asymptotic behaviour of fourth order nonlinear difference equations. Acta Mathematica Sinica 13, 105–115 (1997). https://doi.org/10.1007/BF02560530

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  • DOI: https://doi.org/10.1007/BF02560530

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