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
