scholarly journals Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

2003 ◽  
Vol 41 (6) ◽  
pp. 2197-2209 ◽  
Author(s):  
A. L. Codd ◽  
T. A. Manteuffel ◽  
S. F. McCormick
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Least Squares ◽  
Elliptic Partial Differential Equations ◽  
Order System ◽  
Partial Differential ◽  
First Order ◽  
Nonlinear Elliptic

On the Dirichlet problem for weakly non-linear elliptic partial differential equations

1977 ◽  
Vol 76 (4) ◽  
pp. 283-300 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Weakly Nonlinear ◽  
Partial Derivatives ◽  
Nonlinear Elliptic ◽  
Non Linear

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

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