Multiple equilibria,periodic solutions and a priori bounds for
solutions in superlinear parabolic problems |
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Authors: | Email author" target="_blank">Pavol?QuittnerEmail author |
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Institution: | (1) Institute of Applied Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia |
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Abstract: | Consider the Dirichlet problem for the parabolic equation
in
, where
$\Omega$ is a bounded domain in
and f has superlinear subcritical growth in u.
If f is independent of t and satisfies some
additional conditions then using a dynamical method we find multiple (three, six or infinitely many) nontrivial
stationary solutions. If f has the form
where m is periodic, positive and m,g satisfy some technical
conditions then we prove the existence of a positive periodic solution and
we provide a locally uniform bound for all global solutions. |
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Keywords: | 35B45 35K60 35J65 |
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