文章基本信息

标题：A new application of Schrödinger-type identity to singular boundary value problem for the Schrödinger equation
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作者：Bo Meng
期刊名称：Boundary Value Problems
印刷版ISSN：1687-2762
电子版ISSN：1687-2770
出版年度：2019
卷号：2019
期号：1
页码：1-20
DOI：10.1186/s13661-019-1279-9
出版社：Hindawi Publishing Corporation
摘要：In this paper, we present a modified Schrödinger-type identity related to the Schrödinger-type boundary value problem with mixed boundary conditions and spatial heterogeneities. This identity can be regarded as an $L^{1}$ -version of Fisher–Riesz’s theorem and has a broad range of applications. Using it and fixed point theory in $L^{1}$ -metric spaces, we prove that there exists a unique solution for the singular boundary value problem with mixed boundary conditions and spatial heterogeneities. We finally provide two examples, which show the effectiveness of the Schrödinger-type identity method.
关键词：Boundary value problem; Schrödinger-type identity; Uniqueness