Sabri Bensid, Sidi Mohammed Bouguima
Abstract:
We study the nonlinear elliptic problem with discontinuous nonlinearity
where
is the Heaviside unit function,
are given functions and
is a positive real parameter. The domain
is the unit ball in
with
.
We show the existence of a positive
solution
and a hypersurface separating the region where
from the region where
.
Our method relies
on the implicit function theorem and bifurcation analysis.
Submitted February 22, 2010. Published April 19, 2010.
Math Subject Classifications: 34R35, 35J25.
Key Words: Green function; maximum principle; bifurcation;
free boundary problem.
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Sabri Bensid Department of Mathematics, Faculty of Sciences University of Tlemcen, B.P. 119, Tlemcen 13000, Algeria email: edp_sabri@yahoo.fr | |
Sidi Mohammed Bouguima Department of Mathematics, Faculty of Sciences University of Tlemcen, B.P. 119, Tlemcen 13000, Algeria email: bouguima@yahoo.fr |
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