Ramzi Alsaedi, Habib Maagli, Vicentiu Radulescu, Noureddine Zeddini
Abstract:
In this article, we study the existence and nonexistence of positive bounded
solutions of the Dirichlet problem
where
()
is the upper half-space and
is a positive parameter.
The potential functions p,q are not necessarily bounded, they may change
sign and the functions
are continuous.
By applying the Leray-Schauder fixed point theorem, we establish the
existence of positive solutions for
sufficiently small when
and
.
Some nonexistence results of positive bounded
solutions are also given either if
is sufficiently small
or if
is large enough.
Submitted April 13, 2015. Published June 26, 2015.
Math Subject Classifications: 35B09, 35J47, 35J57, 58C30.
Key Words: Semilinear elliptic system; Leray-Schauder fixed point theorem;
positive bounded solution; indefinite potential.
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Ramzi Alsaedi Department of Mathematics, Faculty of Sciences King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia email: ramzialsaedi@yahoo.co.uk | |
Habib Mâaagli Department of Mathematics, Faculty of Sciences King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia email: abobaker@kau.edu.sa | |
Vicentiu Radulescu Department of Mathematics, Faculty of Sciences King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia email: vicentiu.radulescu@imar.ro | |
Noureddine Zeddini Department of Mathematics, Faculty of Sciences King Abdulaziz University, P.O. Box 80203 Jeddah 21589, Saudi Arabia email: nalzeddini@kau.edu.sa |
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