Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 84, pp. 1-20.

Title: Blow up and asymptotic behavior of solutions for a p(x)-Laplacian equation
 with delay term and variable exponents
       
Authors: Stanislav Antontsev (Lavrentyev Inst. of Hydrodynamics, Novosibirsk, Russia)
         Jorge Ferreira (Federal Fluminense Univ., Rio de Janeiro, Brazil)
         Erhan Piskin (Dicle Univ., Diyarbakir, Turkey)
         Hazal Yuksekkaya (Dicle Univ., Diyarbakir, Turkey)
         Mohammad Shahrouzi (Jahrom Univ., Jahrom, Iran)

Abstract:
In this article, we consider a nonlinear p(x)-Laplacian equation
with time delay and variable exponents. Firstly, we prove the blow up of
solutions. Then, by applying an integral inequality due to Komornik, we
obtain the decay result.

Submitted June 7, 2021. Published October 08, 2021.
Math Subject Classifications: 35B40, 35B44, 35L05.
Key Words: Blow up; decay; variable exponents; delay term.