A new application of Schrödinger-type identity to singular boundary value problem for the Schrödinger equation
Keyword(s):
Abstract 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 $L^{1}$ L 1 -version of Fisher–Riesz’s theorem and has a broad range of applications. Using it and fixed point theory in $L^{1}$ 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.
2014 ◽
Vol 17
(2)
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2012 ◽
Vol 2012
(1)
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2005 ◽
Vol 41
(10)
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pp. 1501-1504
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