Abstract
We establish a nonexistence result of global solutions to the nonlinear evolution equation
(|u|(beta))(tt) - |nu|(alpha)(H)Delta(H)(|u|(beta)) + h(nu)(|u|(q))(t) = f(t, nu)|u|(p) + w(t, nu), nu is an element of H,
where Delta(H) is the Kohn-Laplace operator on the (2N+1)-dimensional Heisenberg group H, |nu|(H) is the distance from nu to the origin, beta, p, q > 0, alpha >= 0, f(t, v) >= 0, h(nu) and w(t, nu) are given functions. Next, we extend this result to the case of systems. Our technique of proof is based on Pohozaev's nonlinear capacity method.