Geodesic
Nonexistence results for a pseudo-hyperbolic equation in the Heisenberg group
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 47J35, 34A34, 35R03
Keywords: nonexistence, nonlinear pseudo-hyperbolic equation, systems of pseudo-hyperbolic equations, Heisenberg group 
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     author = {Kirane, Mokhtar and Ragoub, Lakhdar},
     title = {Nonexistence results for a pseudo-hyperbolic equation in the {Heisenberg} group},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a42/}
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Kirane, Mokhtar; Ragoub, Lakhdar. Nonexistence results for a pseudo-hyperbolic equation in the Heisenberg group. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a42/