scholarly journals On nontrivial solutions of homogeneous Dirichlet problem for partial differential equations in a layer

2018 ◽  
Vol 42 (2) ◽  
pp. 193-207 ◽  
Author(s):  
Z. Nytrebych ◽  
V. Il'kiv ◽  
P. Pukach ◽  
O. Malanchuk
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nontrivial Solutions ◽  
Partial Differential ◽  
Homogeneous Dirichlet Problem

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.

scholarly journals Pointwise bounds for a solution of a nonlinear boundary value problem in partial differential equations

1983 ◽  
Vol 24 (4) ◽  
pp. 366-373
Author(s):  
N. Anderson ◽  
A. M. Arthurs
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Liouville Equation ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Partial Differential ◽  
Nonlinear Boundary Value

AbstractPointwise bounds are obtained for the solution of a Dirichlet problem involving the nonlinear Liouville equation in the plane, Illustrative calculations are performed for a square domain.

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