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 lamé equation utt − ∆eu − div(|∇u|r(x)-2∇u)+|ut|(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.