Electron. J. Diff. Eqns., Vol. 2001(2001), No. 29, pp. 1-17.

A priori estimates for global solutions and multiple equilibria of a superlinear parabolic problem involving measures

Pavol Quittner

We consider a noncoercive elliptic problem in a bounded domain with a power nonlinearity and measure data. It is known that the problem possesses a stable solution and we prove existence of three further solutions. The proof is based on uniform bounds of global solutions of the corresponding parabolic problem and on a topological degree argument.

Submitted December 14, 200. Published May 2, 2001.
Math Subject Classifications: 35B45, 35J65, 35K60.
Key Words: superlinear parabolic equation, semilinear elliptic equation, multiplicity, singular solutions.

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Pavol Quittner
Institute of Applied Mathematics
Comenius University
SK - 84248 Bratislava, Slovakia
e-mail: quittner@fmph.uniba.sk

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