A multiplicity result for a degenerate elliptic equation with critical growth on noncontractible domains

Abstract

In this paper we consider the semilinear problem with critical growth in the Heisenberg group $-\Delta_{_{\mathbb{H}^n}} u = u^{(Q+2)/(Q-2)}+\lambda u$ in $\Omega$, $u> 0$ in $\Omega$, $u=0$ in $\partial\Omega$, and we provide a multiplicity existence result involving Lusternik-Schnirelmann category.