Ramzi Alsaedi
Abstract:
Using some potential theory tools and the Schauder fixed point theorem,
we prove the existence of a positive continuous weak solution
for the fractional system
in a bounded
-domain D in
,
subject to Dirichlet conditions, where
,
,
. The potential functions p,q
are nonnegative and required to satisfy some adequate hypotheses related
to the Kato class
. We also investigate the global
behavior of such solution.
Submitted November 2, 2012. Published January 30, 2013.
Math Subject Classifications: 26A33, 34B27, 35B44, 35B09.
Key Words: Fractional nonlinear systems, Green function, positive solutions,
maximum principle.
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Ramzi Alsaedi Department of Mathematics, College of Science and Arts King Abdulaziz University, Rabigh Campus, P. O. Box 344 Rabigh 21911, Saudi Arabia email: ramzialsaedi@yahoo.co.uk |
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