Global and blow-up solutions to a p-Laplacian equation with nonlocal source

This paper deals with a p-Laplacian equation ut − div(; up−2 u)) = ∫Ωuq(x,t) dx with null Dirichlet boundary conditions in a bounded domain Ω RN, where p > 2, q ≥ 1. Under appropriate hypotheses, we establish local theory of the solution and obtain that the solution either exists globally or blows up in finite time.