Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 12, pp. 1-11.

Nontrivial solutions to the semilinear Kohn-Laplace equation on R^3

Stepan Tersian

The existence of nontrivial solutions to the semilinear Kohn-Laplace equation
$$ -\Delta _Hu+V(P)u=f(u)$$
is considered under appropriate assumptions on $V(P)$ and $f(u)$. Results are obtained using a variational method and a compact-embedding lemma.

Submitted November 26, 1998. Published April 15, 1999.
Math Subject Classification: 35J20, 35J25.
Key Words: Kohn--Laplace equation, homoclinic type solutions, homogeneous spaces, mountain-pass theorem.

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Stepan Tersian
Center of Applied Mathematics and Informatics
University of Rousse
8, Studentska
7017 Rousse, Bulgaria
E-mail: tersian@ami.ru.acad.bg

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