The Characterization of Flat Riemann Spaces as a Boundary Value Problem

1940 ◽  
Vol 19 (1-4) ◽  
pp. 247-259
Author(s):  
T. Y. Thomas
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value

scholarly journals Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem

2007 ◽  
Vol 2007 ◽  
pp. 1-14
Author(s):  
Huting Yuan ◽  
Guang Zhang ◽  
Hongliang Zhao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Constant Number ◽  
Fixed Integer ◽  
Negative Numbers ◽  
Existence Of Positive Solutions

A discrete three-point boundary value problemΔ2xk−1+λfk(xk)=0,k=1,2,…,n, x0=0,axl=xn+1, is considered, where1≤l≤nis a fixed integer,ais a real constant number, andλis a positive parameter. A characterization of the values ofλis carried out so that the boundary value problem has the positive solutions. Particularly, in this paper the constantacan be negative numbers. The similar results are not valid for the three-point boundary value problem of differential equations.

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