TITLE

A Remark on the Existence of Positive Solutions for Some Elliptic Systems

AUTHOR(S)
Afrouzi, G. A.; Rasouli, S. H.
PUB. DATE
June 2006
SOURCE
Advances in Theoretical & Applied Mathematics;2006, Vol. 1 Issue 2, p109
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper we study the existence of positive solutions for the system {-?u = ?f(x, u, v), x ? O, -?v = ?g(x, u, v), x ? O, u = v = 0, x ? O, where ? is the Laplacian operator, ? is a real positive parameter, O is a bounded domain in RN (N = 1) with smooth boundary ?O, and f, g are C� functions satisfying s ? 8 lim f(x,s,s,) = 8 = s ? 8 lim g(x,s,s,) uniformly in x, |(s,t)| ? 8 lim f(x,s,t)/s = s uniformly in x, and |(s,t)| ? 8 lim g(x,s,t)/t = d uniformly in x. In particular we do not assume any sign conditions on f(x, 0, 0) or g(x, 0, 0) for all x ? O. For ? large we prove the existence of a large positive solution. Our approach is based on the method of sub-super solutions.
ACCESSION #
23654816

 

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