Nonexistence of Solutions for a Higher-Order Wave Equation with Delay and Variable-Exponents

In this article, we deal with a higher-order wave equation with delay term and variable exponents. Under suitable conditions, we prove the nonexistence of solutions in a finite time. Generally, the problems with variable exponents arise in many branches in sciences such as nonlinear elasticity theory, electrorheological fluids and image processing. Time delays often appear in many practical problems such as thermal, biological, chemical, physical and economic phenomena.