Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equationu t + ( − Δ H ) mu t + ( − Δ H ) m u = | u | p , ( η , t ) ∈ H × ( 0 , ∞ ) ,whereΔ His the Kohn‐Laplace operator on the (2 N + 1)‐dimensional Heisenberg group H , m ≥1, p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.