Blow up of solutions for a r(x)-Laplacian Lam'{e} equation with variable-exponent nonlinearities and arbitrary initial energy level

In this paper, we consider the nonlinear r(x)−Laplacian Lam'{e} equation utt−Δeu−div(|∇u|r(x)−2∇u)+|ut|m(x)−2ut=|u|p(x)−2u in a smoothly bounded domain Ω⊆Rn, n≥1, where r(.), m(.) and p(.) are continuous and measurable functions. Under suitable conditions on variable exponents and initial data, the blow-up of solutions is proved with negative initial energy as well as positive.