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We establish a nonexistence result of global solutions to the nonlinear evolution equation (|u| β ) tt  − |ϑ| α  H Δ H (|u| β ) + h(ϑ)(|u| q ) t  = f(t, ϑ)|u| p  + w(t, ϑ), ϑ ∈ H, where ΔH is the Kohn-Laplace operator on the (2N+1)-dimensional Heisenberg group H, |ϑ| H  is the distance from ϑ to the origin, β, p, q &gt; 0, α ≥ 0, f(t, v) ≥ 0, h(ϑ) and w(t, ϑ) 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.

Nonexistence results for a class of evolution equations in the Heisenberg group