We prove some existence of positive solutions to the semilinear elliptic system
in the half space , , subject to some Dirichlet conditions, where and are nonnegative parameters. The functions are nonnegative continuous monotone on and the potentials are nonnegative and satisfy some hypotheses related to the Kato class .
Submitted March 16, 2010. Published January 21, 2011.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Green function; Kato class; elliptic systems; positive solutions.
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| Noureddine Zeddini |
Department of Mathematics, College of Sciences and Arts
King Abdulaziz University, P.O. Box 344. Rabigh 21911, Saudi Arabia.
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
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