Blow-up Results for Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term

We obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problem where λ > 0 is small, u ∈ L (ℝ ) with u ≥ 0, when . For this purpose we use the method of “test function”.