On some Semilinear Periodic Parabolic Problems
T. Godoy, Uriel Kaufmann · OpenstarTs (Univeristy of Trieste https://www.units.it/) · 2006
Let $\\Omega \\subset \\mathbb R^N$ a smooth bounded domain. We study existence and nonexistence of positive solutions for some semilinear Dirichlet periodic parabolic problems of the form $Lu = h(x,t,u)$ in $\\Omega\\times \\mathbb R$ for a class of Caratheodory functions $h : \\Omega\\times \\mathbb R \\times [0,\\infty) \\rightarrow \\mathbbR$ such that h (., 0) = 0 and $\\lim_{\\xi\\rightarrow 0^+}\\xi^{ −1}h (.,\\xi) = 0$ or $-\\infty$. All results remain true for the corresponding elliptic problems.