BLOW-UP AND GLOBAL EXISTENCE OF SOLUTIONS FOR HIGHER-ORDER KIRCHHOFF-TYPE EQUATIONS WITH VARIABLE EXPONENTS

Abstract

This paper is concerned with the blow-up and global existence of solutions for Higher-Order Kirchhoff-Type Equations with variable exponents. Under suitable assumptions, we prove some finite time blow-up results for certain solutions with positive initial energy by using a concavity-type method. This work improves and generalizes several interesting recent blow-up results on wave equations in particular on Kichhoff-type equations. We also show the global existence of solutions under appropriate conditions.