An existence theorem and application to a non-linear elliptic boundary value problem

2006 ◽  
pp. 398-408
Author(s):  
A. J. B. Potter
Keyword(s):  
Boundary Value Problem ◽  
Existence Theorem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary

An elliptic boundary value problem for strongly non-linear equations in unbounded domains

1977 ◽  
Vol 77 (3-4) ◽  
pp. 217-230 ◽  
Author(s):  
Vesa Mustonen
Keyword(s):  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary ◽  
Non Linear Equations

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.

scholarly journals 3.—A Criterion for the Existence of Solutions of Non-linear Elliptic Boundary Value Problems

1976 ◽  
Vol 74 ◽  
pp. 49-54 ◽  
Author(s):  
Johanna Deuel ◽  
Peter Hess
Keyword(s):  
Weak Solution ◽  
General Type ◽  
Existence Of Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Lower Solution ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Elliptic Boundary

SynopsisBy a new method it is proved that a non-linear elliptic boundary value problem of rather general type admits a weak solution lying between a given weak lower solution ϕ and a given weak upper solution ψ≧ϕ

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