Jacques Giacomoni, Jyotshana V. Prajapat, Mythily Ramaswamy
Abstract:
In this paper, we study the semilinear elliptic problem with critical
nonlinearity and an indefinite weight function, namely
in a smooth open bounded domain
,
with Dirichlet boundary conditions and for
.
Under suitable assumptions on the weight function, we obtain
the positive solution branch, bifurcating from the first
eigenvalue
. For
,
we get similar results for
where
is bounded and superlinear near zero.
Published February 28, 2007.
Math Subject Classifications: 35J60, 35B45, 35B33, 35B32.
Key Words: Critical indefinite nonlinearity; bifurcation; a priori estimates.
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Jacques Giacomoni MIP-CEREMATH/bat C, Manufacture des Tabacs Allée de Brienne 21 31000 Toulouse, France email: giacomo4@yahoo.fr | |
Jyotshana V. Prajapat School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai 400 005, India email: jyotsna@math.tifr.res.in | |
Mythily Ramaswamy TIFR Center, IISc. Campus Bangalore 560 012, India email: mythily@math.tifrbng.res.in |
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