scholarly journals Quasistationary distributions for one-dimensional diffusions with singular boundary points

2019 ◽  
Vol 129 (5) ◽  
pp. 1659-1696
Author(s):  
Alexandru Hening ◽  
Martin Kolb
Keyword(s):  
Singular Boundary ◽  
One Dimensional ◽  
Boundary Points ◽  
Quasistationary Distributions

The solvability of an elliptic system under a singular boundary condition

2006 ◽  
Vol 136 (3) ◽  
pp. 509-546 ◽  
Author(s):  
J. García-Melián ◽  
J. Sabina de Lis ◽  
R. Letelier-Albornoz
Keyword(s):  
Boundary Condition ◽  
Elliptic System ◽  
Positive Solutions ◽  
Detailed Account ◽  
Singular Boundary ◽  
Dimensional Problem ◽  
One Dimensional ◽  
All Solutions ◽  
The One ◽  
Singular Boundary Condition

In this work we are considering both the one-dimensional and the radially symmetric versions of the elliptic system Δu = vp, Δv = uq in Ω, where p, q > 0, under the boundary condition u|∂Ω = +∞, v|∂Ω = +∞. It is shown that no positive solutions exist when pq ≤ 1, while we provide a detailed account of the set of (infinitely many) positive solutions if pq > 1. The behaviour near the boundary of all solutions is also elucidated, and symmetric solutions (u, v) are completely characterized in terms of their minima (u(0), v(0)). Non-symmetric solutions are also deeply studied in the one-dimensional problem.

Singular boundary points of analytic functions

1980 ◽  
Vol 28 (6) ◽  
pp. 859-864
Author(s):  
S. V. Kolesnikov
Keyword(s):  
Analytic Functions ◽  
Singular Boundary ◽  
Boundary Points
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