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Linearization near a locally nonunique invariant manifold
Existence of stable and unstable periodic solutions for semilinear parabolic problems
| 1. | School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia |
| 2. | Department of Mathematics, Yokohama National University, 156 Tokiwadai Hodogaya-ku - Yokohama |
$\frac{\partial u}{\partial t} - \Delta u = g(x,u) + h( t, x ),\quad \text{in} \quad (0,T) \times \Omega$
$u=0 ,\quad \text{on}\quad (0,T) \times \partial \Omega$
$u(0) = u(T),\quad \text{in} \quad \overline \Omega$
where $\Omega \subset R^N$ is a bounded domain with a smooth boundary, $g:\overline{\Omega} \times R \rightarrow R$ is a continuous function such that $g(x,\cdot )$ has a superlinear growth for each $x \in \overline{\Omega} $ and $h:(0,T) \times \Omega \to R$ is a continuous function.
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