  Based on the concepts of a generalized critical point and the corresponding
generalized P.S. condition introduced by Duong Minh Duc[1], we have proved a
new $Z_2$ index theorem and get a result on multiplicity of generalized
critical points. Using the result and a quite standard variational method, it
is found that the equation $$ -\Delta_{H^n} u=|u|^{p-1} u ~ x\in H^n $$ has
infinite positive solutions. Our approach can also be applied to study more
general nonlinear problems.
