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
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