Electron. J. Diff. Equ., Vol. 2015 (2015), No. 110, pp. 1-9.

Nonexistence results for a pseudo-hyperbolic equation in the Heisenberg group

Mokhtar Kirane, Lakhdar Ragoub

Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear pseudo-hyperbolic equation
 u_{tt} -\Delta_{\mathbb H} u_{tt}-\Delta_{\mathbb H} u=|u|^p, \quad
  (\eta, t) \in   \mathbb{H} \times (0,\infty), \;  p>1,
where $\Delta_\mathbb{H}$ is the Kohn-Laplace operator on the $(2N+1)$-dimensional Heisenberg group $\mathbb{H}$. Then, this result is extended to the case of a $2 \times 2$-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.

Submitted January 5, 2015. Published April 22, 2015.
Math Subject Classifications: 47J35, 34A34, 35R03.
Key Words: Nonexistence; nonlinear pseudo-hyperbolic equation; systems of pseudo-hyperbolic equations; Heisenberg group.

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Mokhtar Kirane
Laboratoire de Mathématiques, Image et Applications
Pôle Sciences et Technologies
Université de La Rochelle
Avenue M. Crépeau, 17042 La Rochelle, France
email: mkirane@univ-lr.fr
Lakhdar Ragoub
Al Yamamah University
College of Computers and Information Systems
P.O. Box 45180, Riyadh 11512, Saudi Arabia
email: l_ragoub@yu.edu.sa

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