PERIODIC SOLUTIONS IN SUPERLINEAR PARABOLIC PROBLEMS
Juraj Húska · 2002
Consider the Dirichlet problem for the parabolic equation ut = ∆u + m(t)g(x, u) in Ω × (0,∞) where Ω is a smoothly bounded, convex domain in Rn 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.