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<p>We establish a three circles inequality for a solution to a class of Schrödinger type equation on a product <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3201_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(N \times [0,\infty )\)</EquationSource> </InlineEquation>. As an application, we show that the space of solutions for a class of Schrödinger type operators with bounded coefficients on a complete noncompact manifold with finitely many cylindrical ends that grow at most exponentially at infinity is finite dimensional.</p>

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Three circles theorem for a class of Schrödinger type equations on cylindrical ends

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Lin Wang,
  • Miaomiao Zhu

摘要

We establish a three circles inequality for a solution to a class of Schrödinger type equation on a product \(N \times [0,\infty )\) . As an application, we show that the space of solutions for a class of Schrödinger type operators with bounded coefficients on a complete noncompact manifold with finitely many cylindrical ends that grow at most exponentially at infinity is finite dimensional.