ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXI, 1(2002)
p. 19

Periodic solutions in superlinear parabolic problems
J. Huska

Abstract.  Consider the Dirichlet problem for the parabolic equation $u_t=\Delta u+m(t)g(x,u)$ in $\Omega\times(0,\infty)$ where $\Omega$ is a smoothly bounded, convex domain in $\mathbb R ^n$ and $g$ has superlinear subcritical growth in $u$. If $m$ is periodic, positive and $m,g$ satisfy some technical conditions then we prove the existence of a positive periodic solution.

AMS subject classification:  35B45, 35K60
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