Abstract
We consider exterior boundary value problems with nontrivial boundary conditions, including three types of semilinear equations: heat equation, wave equation and damped wave equation. Using a test function approach with a choice of a suitable family of test functions, we obtain the critical exponents in the sense of Fujita for the considered problems. Our obtained results close some open questions from the literature. (C) 2018 Elsevier Ltd. All rights reserved.