Abstract
We consider three types of semilinear equations (elliptic, parabolic and hyperbolic) posed in the N-dimensional exterior domain R-N\D, where N >= 2 and D is the closed unit ball in R-N. A nontrivial Robin boundary condition is imposed on the boundary of D. Using a test function approach with judicious choices of the test functions, we show that the considered problems share a common critical behavior. We discuss separately the cases N = 2 and N >= 3. Moreover, in the case N >= 3, the dependence of the critical exponent on initial data is discussed. To the best our knowledge, the study of the critical behaviorin an exterior domain with a nontrivial Robin boundary condition has never been studied in the literature. (C) 2020 Elsevier Inc. All rights reserved.