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<p>We study the uniqueness of solutions to the stationary Schrödinger equation with potential on infinite graphs, within suitable weighted <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell ^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> spaces. The potential is allowed to vanish at infinity at a controlled rate. Our results extend those in [<CitationRef CitationID="CR20">20</CitationRef>] by considering a broader class of potentials, by removing the assumption that the potential is bounded away from zero.</p>

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Uniqueness for the Schrödinger equation on graphs with potential vanishing at infinity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月28日

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  • Fabio Punzo,
  • Marcello Svagna

摘要

We study the uniqueness of solutions to the stationary Schrödinger equation with potential on infinite graphs, within suitable weighted \(\ell ^p\) ℓ p spaces. The potential is allowed to vanish at infinity at a controlled rate. Our results extend those in [20] by considering a broader class of potentials, by removing the assumption that the potential is bounded away from zero.