On the Number of Positive Solutions of a Critical Elliptic Equation in Divergence Form

We establish results concerning the existence and multiplicity of positive solutions for the problem $$-\text{div}(a(\varepsilon x)|\nabla u|^{p-2}\nabla u) + |u|^{p-2}u= f(u)+|u|^{p^{*}-2}u~~\text{in }\mathbb{R}^N,~~~ u \inW^{1,p}(\mathbb{R}^N),$$where $2 \leq p