Abstract
We show that every Lie point symmetry of semilinear Kohn-Laplace equations with a power-law nonlinearity on the Heisenberg group H 1 is a divergence symmetry if and only if the corresponding exponent takes a critical value.
This is a preview of subscription content, log in via an institution to check access.
References
Garofalo, N. and Lanconelli, E., Existence and Nonexistence Results for Semilinear Equations on the Heisenberg Group, Indiana Univ. Math. J., 1992, vol. 41, pp. 71–98.
Pohozaev, S.I. and Veron, L., Nonexistence Results of Solutions of Semilinear Differential Inequalities on the Heisenberg Group, Manuscripta Math., 2000, vol. 102, pp. 85–99.
Lanconelli, E., Critical Semilinear Equations on the Heisenberg Group, Workshop on Partial Differential Equations (Ferrara, 1999), Ann. Univ. Ferrara Sez. VII (N.S.), 1999, vol. 45,Suppl, pp. 187–195.
Olver, P.J., Application of Lie Groups to Differential Equations, GTM 107, New York, 1986.
Ovsiannikov, L., Group Analysis of Differential Equations, London, 1982.
Bozhkov, Y. and Freire, I.L., Group Classification of Semilinear Kohn-Laplace Equations, Nonlinear Anal., 2008, vol. 68, pp. 2552–2568.
Bozhkov, Y. and Freire, I.L., Conservations Laws for Critical Kohn-Laplace Equations on the Heisenberg Group, J. Nonlinear Math. Phys., 2008, vol. 15, pp. 35–47.
Bozhkov, Y., Noether Symmetries and Critical Exponents, Sigma Symmetry Integrability Geom. Methods Appl., 2005, vol. 1, paper 022.
Author information
Authors and Affiliations
Additional information
Original Russian Text © Yu.D. Bozhkov, I.L. Freire, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 8, pp. 1196–1200.
Rights and permissions
About this article
Cite this article
Bozhkov, Y.D., Freire, I.L. Divergence symmetries of critical Kohn-Laplace equations on Heisenberg groups. Diff Equat 47, 1210–1214 (2011). https://doi.org/10.1134/S0012266111080143
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0012266111080143