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

Abstract

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.

Keywords

• Kohn--Laplace equation
• homoclinic type solutions
• homogeneous spaces
• mountain-pass theorem.