2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63134Based 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 $$ -Δ_{H^n} u=|u|^{p-1} u ~ x\in H^n $$ has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.12 pages, 0 figuresAnalysis of PDEstext