scholarly journals An Existence Theorem for a Class of Non-Linear Integral Equations with Applications to a Non-Linear Elliptic Boundary Value Problem

1968 ◽  
Vol 18 (5) ◽  
pp. 411-421
Author(s):  
Charles Coffman
Keyword(s):  
Boundary Value Problem ◽  
Existence Theorem ◽  
Integral Equations ◽  
Elliptic Boundary ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Elliptic Boundary ◽  
Linear Integral Equations

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.

A Quasi-Linear Elliptic Boundary Value Problem

1966 ◽  
Vol 18 ◽  
pp. 1105-1112 ◽  
Author(s):  
R. A. Adams
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Elliptic Boundary ◽  
Classical Solutions ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Open Set ◽  
Image Position ◽  
Linear Elliptic Boundary ◽  
Typical Point

Let Ω be a bounded open set in Euclidean n-space, En. Let α = (α1, … , an) be an n-tuple of non-negative integers;and denote by Qm the set ﹛α| 0 ⩽ |α| ⩽ m}. Denote by x = (x1, … , xn) a typical point in En and putIn this paper we establish, under certain circumstances, the existence of weak and classical solutions of the quasi-linear Dirichlet problem1

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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