Abstract
We investigate the large time behavior of solutions to a class of inhomoge-neous hyperbolic inequalities involving combined nonlinearities of the form |u|p + integral t 10 (t-s)Sigma-1| backward difference u(s, x)|qds+w(x), where p, q > 1 and Sigma > 0. We show that, if Gamma(Sigma) w has a positive average, then the considered class admits no global weak solution. Our approach is based on nonlinear capacity estimates specifically adapted to the nonlocal setting of our problem.(c) 2022 Elsevier Ltd. All rights reserved.