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

Salvador Sánchez-Perales, Francisco J. Mendoza-Torres (2020)

Czechoslovak Mathematical Journal

In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation - y ' ' + q y = 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.

Boundary value problems with compatible boundary conditions

George L. Karakostas, P. K. Palamides (2005)

Czechoslovak Mathematical Journal

If Y is a subset of the space n × n , we call a pair of continuous functions U , V Y -compatible, if they map the space n into itself and satisfy U x · V y 0 , for all ( x , y ) Y with x · y 0 . (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential n -dimensional system is investigated, provided the boundary conditions are given via...

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