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- W2809105924 abstract "Consider the first-order delay difference equation with a constant argument <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi mathvariant=normal>Δ</mml:mi><mml:mi>x</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi>p</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfenced><mml:mi>x</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0</mml:mn><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mo> </mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0,1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant=normal>2</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo></mml:math> and the delay difference equation with a variable argument <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mi mathvariant=normal>Δ</mml:mi><mml:mi>x</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi>p</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfenced><mml:mi>x</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>τ</mml:mi><mml:mfenced separators=|><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0</mml:mn><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mo> </mml:mo><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant=normal>0,1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant=normal>2</mml:mn><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo></mml:math> where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>p</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math> is a sequence of nonnegative real numbers, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math> is a positive integer, <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi mathvariant=normal>Δ</mml:mi><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant=normal>1</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo>-</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>,</mml:mo></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>τ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math> is a sequence of integers such that <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mi>τ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>≤</mml:mo><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant=normal>1</mml:mn></mml:math> for all <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>n</mml:mi><mml:mo>≥</mml:mo><mml:mn mathvariant=normal>0</mml:mn></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:msub><mml:mrow><mml:mi mathvariant=normal>l</mml:mi><mml:mi mathvariant=normal>i</mml:mi><mml:mi mathvariant=normal>m</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant=normal>∞</mml:mi></mml:mrow></mml:msub><mml:mi>τ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mi mathvariant=normal>∞</mml:mi></mml:math>. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given." @default.
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- W2809105924 date "2018-06-21" @default.
- W2809105924 modified "2023-09-26" @default.
- W2809105924 title "Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument" @default.
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- W2809105924 doi "https://doi.org/10.1155/2018/9416319" @default.
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