The initial value problem for the Schrödinger equation involving the Henstock–Kurzweil integral

• Salvador Sánchez Perales ^[1]
  1. [1] Universidad Tecnológica de la Mixteca

     Universidad Tecnológica de la Mixteca

     México

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 58, Nº. 2, 2017, págs. 297-306
• Idioma: inglés
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• Resumen

  • Let L be the one-dimensional Schrödinger operator defined by Ly=−y′′+qy. We investigate the existence of a solution to the initial value problem for the differential equation (L−λ)y=g, when q and g are Henstock–Kurzweil integrable functions on [a,b]. Results presented in this article are generalizations of classical results for the Lebesgue integral.