Second-Order Asymptotic Optimality and Positive Solutions of Schrödinger’s Equation

1986 ◽  
Vol 30 (2) ◽  
pp. 333-363 ◽  
Author(s):  
B. Ya. Levit
Keyword(s):  
Positive Solutions ◽  
Asymptotic Optimality ◽  
Second Order ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

Pushing the limit for the grid-based treatment of Schrödinger's equation: a sparse Numerov approach for one, two and three dimensional quantum problems

2016 ◽  
Vol 18 (46) ◽  
pp. 31521-31533 ◽  
Author(s):  
Ulrich Kuenzer ◽  
Jan-Andrè Sorarù ◽  
Thomas S. Hofer
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Second Order ◽  
Special Focus ◽  
Schrödinger’S Equation ◽  
Numerov Method ◽  
Schrödinger's Equation ◽  
Grid Based

The general Numerov method employed to numerically solve ordinary differential equations of second order was adapted with a special focus on matrix sparsity and applications in higher dimensions.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

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