Blow‐up and decay of solutions for a viscoelastic Kirchhoff‐type equation with distributed delay and variable exponents

Abstract

In this article, we focussed on a nonlinear viscoelastic Kirchhoff‐type equation with distributed delay and variable‐exponents. The blow‐up solutions of the problem are proved under suitable hypothesis, and by using an integral inequality due to Komornik, the general decay outcome is obtained in the case .