A new application of Schrodinger-type identity to singular boundary value problem for the Schrodinger equation

In this paper, we present a modified Schrodinger-type identity related to the Schrodinger-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 Schrodinger-type identity method.