Upper and lower bounds to the Schrödinger equation eigenvalues

1990 ◽  
Vol 37 (6) ◽  
pp. 747-752 ◽  
Author(s):  
Francisco M. Fernández
Keyword(s):  
Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
Upper And Lower Bounds

Upper and lower bounds for the Schrödinger-equation eigenvalues

1986 ◽  
Vol 116 (9) ◽  
pp. 407-409 ◽  
Author(s):  
F.M. Fernandez ◽  
J.F. Ogilvie ◽  
R.H. Tipping
Keyword(s):  
Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
Upper And Lower Bounds

scholarly journals Sharp blowup rate for NLS with a repulsive harmonic potential

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rui Zhou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Harmonic Potential ◽  
Upper And Lower Bounds ◽  
Singular Solutions ◽  
Blowup Rate ◽  
Nonlinear Schrödinger

AbstractIn this paper, we are concerned with the blowup solutions of the $L^{2}$ L 2 critical nonlinear Schrödinger equation with a repulsive harmonic potential. By using the results recently obtained by Merle and Raphaël and by Carles’ transform we establish in a quite elementary way universal and sharp upper and lower bounds of the blowup rate for the blowup solutions of the aforementioned equation. As an application, we derive upper and lower bounds on the $L^{r}$ L r -norms of the singular solutions.

Tight upper and lower bounds for energy eigenvalues of the Schrödinger equation

1989 ◽  
Vol 39 (4) ◽  
pp. 1605-1609 ◽  
Author(s):  
Francisco M. Fernández ◽  
Q. Ma ◽  
R. H. Tipping
Keyword(s):  
Schrödinger Equation ◽  
Lower Bounds ◽  
Schrodinger Equation ◽  
Upper And Lower Bounds ◽  
Energy Eigenvalues
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