Jacques Giacomoni, Jyotshana V. Prajapat, Mythily Ramaswamy
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
| Jyotshana V. Prajapat |
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai 400 005, India
| Mythily Ramaswamy |
TIFR Center, IISc. Campus
Bangalore 560 012, India
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