Geodesic
Periodic solutions in superlinear parabolic problems
Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 1 
J. Huska. Periodic solutions in superlinear parabolic problems. Acta mathematica Universitatis Comenianae, Tome 71 (2002) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2002_71_1_a3/
@article{AMUC_2002_71_1_a3,
     author = {J. Huska},
     title = {Periodic solutions in superlinear parabolic problems},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2002},
     volume = {71},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2002_71_1_a3/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.