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<p>The present paper proposes a new concept of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\lambda (t,s)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dichotomy, which includes ordinary dichotomy, exponential dichotomy, algebraic dichotomy and (<i>h</i>,&#xa0;<i>k</i>)-dichotomy, and so on. We establish the robustness of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\lambda (t,s)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dichotomy on Banach spaces by means of a novel dichotomy inequality with <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\lambda (t,s)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> type and other interesting assumptions.</p>

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\(\lambda (t,s)\)-Dichotomy and its Robustness on Banach Spaces

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Huiyang Zhang,
  • Weijie Lu,
  • Lingling Liu

摘要

The present paper proposes a new concept of \(\lambda (t,s)\) λ ( t , s ) -dichotomy, which includes ordinary dichotomy, exponential dichotomy, algebraic dichotomy and (h, k)-dichotomy, and so on. We establish the robustness of \(\lambda (t,s)\) λ ( t , s ) -dichotomy on Banach spaces by means of a novel dichotomy inequality with \(\lambda (t,s)\) λ ( t , s ) type and other interesting assumptions.