Global nonexistence of solutions for von Karman equations with variable exponents

We consider the von Karman equations with variable exponents: utt+Δ2u+a|ut|m(⋅)−2ut=[u,F(u)]+b|u|p(⋅)−2uwhere a and b are positive constants and the exponents m(⋅) and p(⋅) are given measurable functions. There are many literatures on the blow-up result of solutions for the wave equation. However, to the best of our knowledge, there is no blow-up result of solutions for von Karman equations. We investigate a finite time blow-up result of solutions with nonpositive initial energy as well as positive initial energy.