Local and global nonexistence of solutions to nonlinear hyperbolic inequalities Original Research Article

We obtain sufficient conditions for the nonsolvability of View the MathML source , where lm is a homogeneous linear partial differential operator of order m and p >1. For example, we prove that for any T >0 the problem, with ut(x,0) = u1, ϕ(r) = |rz.sfnc;q−1, 0 < q ≤ 1 and h(x) = |x|, γ >0, has no solution if lim|x|→∞u1(x)|x|γq/(p−q) = ∞.