On the solvability of boundary value problems for the stationary Schrödinger equation in unbounded domains on Riemannian manifolds

2015 ◽  
Vol 51 (6) ◽  
pp. 738-744 ◽  
Author(s):  
S. A. Korol’kov
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problems ◽  
Riemannian Manifolds ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Unbounded Domains ◽  
Stationary Schrödinger Equation

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

2019 ◽  
Vol 70 (2) ◽  
pp. 519-537 ◽  
Author(s):  
Salvador Sánchez-Perales ◽  
Francisco J. Mendoza-Torres
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problems ◽  
Schrodinger Equation ◽  
Boundary Value

scholarly journals Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

2009 ◽  
Vol 465 (2111) ◽  
pp. 3341-3360 ◽  
Author(s):  
Guillaume Michel Dujardin
Keyword(s):  
Schrödinger Equation ◽  
Asymptotic Behaviour ◽  
Boundary Value Problems ◽  
Boundary Data ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Half Line ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

This paper deals with the asymptotic behaviour of the solutions of linear initial boundary value problems with constant coefficients on the half-line and on finite intervals. We assume that the boundary data are periodic in time and we investigate whether the solution becomes time-periodic after sufficiently long time. Using Fokas’ transformation method, we show that, for the linear Schrödinger equation, the linear heat equation and the linearized KdV equation on the half-line, the solutions indeed become periodic for large time. However, for the same linear Schrödinger equation on a finite interval, we show that the solution, in general, is not asymptotically periodic; actually, the asymptotic behaviour of the solution depends on the commensurability of the time period T of the boundary data with the square of the length of the interval over π .

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