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Periodic solutions in superlinear parabolic problems. (English) Zbl 1049.35026
Summary: 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.

MSC:
35B10 Periodic solutions to PDEs
35B45 A priori estimates in context of PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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