Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 519-537, 2020


Boundary value problems for the Schrödinger equation involving the Henstock-Kurzweil integral

Salvador Sánchez-Perales, Francisco J. Mendoza-Torres

Received August 24, 2018.   Published online December 12, 2019.

Abstract:  In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation $-y"+qy=f$, where $q$ and $f$ are Henstock-Kurzweil integrable functions on $[a,b]$. Results presented in this article are generalizations of the classical results for the Lebesgue integral.
Keywords:  Henstock-Kurzweil integral; Schrödinger operator; ${\rm ACG}_*$-function; bounded variation function
Classification MSC:  26A39, 34B24, 26A45
DOI:  10.21136/CMJ.2019.0388-18


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Affiliations:   Salvador Sánchez-Perales (corresponding author), Instituto de Fisica y Matemáticas, Universidad Tecnológica de la Mixteca, Carretera a Acatlima Km. 2.5, Acatlima, 69000 Huajuapan de León, Oaxaca, Mexico, e-mail: es21254@yahoo.com.mx; Francisco J. Mendoza-Torres, Facultad de Ciencias Fisico Matemáticas, Benemérita Universidad Autónoma de Puebla, Av San Claudio, Cd Universitaria, Jardines de San Manuel, 72572 Puebla, Mexico, e-mail: jmendoza2@fcfm.buap.mx


 
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