Existence and blow-up of solutions for von Karman equations with time delay and variable exponents

摘要

We study the von Karman equations with time delay and variable exponents:utt+Δ2u+a|ut|q(·)−2ut+b|ut(t−τ)|q(·)−2ut(t−τ)=δ[u,F(u)]+c|u|p(·)−2uwhere a, δ and c are positive constants, b is a real number, τ > 0 represents the time delay and the exponents p(·) and q(·) are given measurable functions. For the blow-up result of solutions for the wave equation, many authors have been investigated. But there are few works on blow-up of solutions for von Karman equations. We show the blow-up result of solutions with positive initial energy as well as non-positive initial energy for the von Karman equations with time delay and variable exponents.