Michinori Ishiwata, Takayoshi Ogawa, Futoshi Takahashi
We consider the following nonlinearly perturbed version of the elliptic-parabolic system of Keller-Segel type:
where . It has already been shown that the system admits a positive solution for a small nonnegative initial data in which corresponds to the local minimum of the associated energy functional to the elliptic part of the system. In this paper, we show that for a radially symmetric nonnegative initial data, there exists another positive solution which corresponds to the critical point of mountain-pass type. The -component of the solution bifurcates from the unique positive radially symmetric solution of in .
Submitted August 22, 2008. Published February 16, 2009.
Math Subject Classifications: 35K15, 35K55, 35Q60, 78A35.
Key Words: Multiple existence; elliptic-parabolic system; unconditional uniqueness.
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| Michinori Ishiwata |
Common Subject Division, Muroran Institute of Technology
Muroran 050-8585, Japan
| Takayoshi Ogawa |
Mathematical Institute, Tohoku University
Sendai 980-8578, Japan
| Futoshi Takahashi |
Graduate School of Science, Osaka City University
Osaka 558-8585, Japan
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