A Parallel Newton Multigrid Method for High Order Finite Elements and Its Application to Numerical Existence Proofs for Elliptic Boundary Value Equations

1996 ◽  
Vol 76 (3) ◽  
pp. 175-180 ◽  
Author(s):  
Chr. Wieners
Keyword(s):  
Finite Elements ◽  
Multigrid Method ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
High Order ◽  
Elliptic Boundary Value ◽  
Existence Proofs

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

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