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On the oscillatory properties of the solutions of a class of integro-differential equations of neutral type

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  • D. D. Bainov
  • A. D. Myshkis
  • A. I. Zahariev

Abstract

In the present paper the oscillatory properties of the solutions of the equation [ ( L x ) ( t ) ] ( n ) + ∫ I t K ( t , s , x ( s ) ) d s = 0 are investigated where n ≥ 1 , L is an operator of the difference type, I t ⊂ ℝ , K : D K → ℝ , D K ⫅ ℝ 3 , x : [ α x , ∞ ] → ℝ . Under natural conditions imposed on L , I t and K it is proved that for n even all ultimately nonzero solutions oscillate and for n odd they either oscillate or tend to zero as t → ∞ .

Suggested Citation

  • D. D. Bainov & A. D. Myshkis & A. I. Zahariev, 1992. "On the oscillatory properties of the solutions of a class of integro-differential equations of neutral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 15, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:163126
    DOI: 10.1155/S0161171292000140
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