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<p>An abstract version of the celebrated inequality is described by means of the spectral bound of an operator defined on a Banach lattice. As a consequence, uniqueness and continuous dependence results for the general semilinear problem <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Lu=N(u)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>L</mi> <mi>u</mi> <mo>=</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are established and a connection with the maximum principle is explored.</p>

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An abstract Gronwall inequality on a Banach lattice

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • P. Amster,
  • J. Epstein

摘要

An abstract version of the celebrated inequality is described by means of the spectral bound of an operator defined on a Banach lattice. As a consequence, uniqueness and continuous dependence results for the general semilinear problem \(Lu=N(u)\) L u = N ( u ) are established and a connection with the maximum principle is explored.